MinT - Best Known (72, 82, s)-Nets in Base 32

Best Known (72, 82, s)-Nets in Base 32

(72, 82, 6712320)-Net over F₃₂ — Constructive and digital

Digital (72, 82, 6712320)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 0, 209760)-net over F₃₂, using
  - s-reduction based on digital (0, 0, s)-net over F₃₂ with arbitrarily large s, using
    - arbitrary set of 32⁰ points [i]
2. digital (0, 0, 209760)-net over F₃₂ (see above)
3. digital (0, 0, 209760)-net over F₃₂ (see above)
4. digital (0, 0, 209760)-net over F₃₂ (see above)
5. digital (0, 0, 209760)-net over F₃₂ (see above)
6. digital (0, 0, 209760)-net over F₃₂ (see above)
7. digital (0, 0, 209760)-net over F₃₂ (see above)
8. digital (0, 0, 209760)-net over F₃₂ (see above)
9. digital (0, 0, 209760)-net over F₃₂ (see above)
10. digital (0, 0, 209760)-net over F₃₂ (see above)
11. digital (0, 0, 209760)-net over F₃₂ (see above)
12. digital (0, 0, 209760)-net over F₃₂ (see above)
13. digital (0, 0, 209760)-net over F₃₂ (see above)
14. digital (0, 0, 209760)-net over F₃₂ (see above)
15. digital (0, 0, 209760)-net over F₃₂ (see above)
16. digital (0, 0, 209760)-net over F₃₂ (see above)
17. digital (0, 0, 209760)-net over F₃₂ (see above)
18. digital (0, 0, 209760)-net over F₃₂ (see above)
19. digital (0, 0, 209760)-net over F₃₂ (see above)
20. digital (0, 0, 209760)-net over F₃₂ (see above)
21. digital (0, 0, 209760)-net over F₃₂ (see above)
22. digital (0, 0, 209760)-net over F₃₂ (see above)
23. digital (0, 1, 209760)-net over F₃₂, using
  - s-reduction based on digital (0, 1, s)-net over F₃₂ with arbitrarily large s, using
    - construction for strength kÂ =Â 1 [i]
24. digital (0, 1, 209760)-net over F₃₂ (see above)
25. digital (0, 1, 209760)-net over F₃₂ (see above)
26. digital (0, 1, 209760)-net over F₃₂ (see above)
27. digital (0, 1, 209760)-net over F₃₂ (see above)
28. digital (3, 5, 209760)-net over F₃₂, using
  - s-reduction based on digital (3, 5, 1082401)-net over F₃₂, using
    - kÂ =Â 2 construction [i]
29. digital (3, 5, 209760)-net over F₃₂ (see above)
30. digital (4, 7, 209760)-net over F₃₂, using
  - s-reduction based on digital (4, 7, 1050624)-net over F₃₂, using
    - net defined by OOA [i] based on linear OOA(32⁷, 1050624, F₃₂, 3, 3) (dual of [(1050624, 3), 3151865, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(32⁷, 1050624, F₃₂, 2, 3) (dual of [(1050624, 2), 2101241, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(32⁷, 1050624, F₃₂, 3) (dual of [1050624, 1050617, 4]-code or 1050624-cap in PG(6,32)), using
        product of two caps with tangent hyperplane [i]
31. digital (12, 17, 209760)-net over F₃₂, using
  - s-reduction based on digital (12, 17, 524289)-net over F₃₂, using
    - net defined by OOA [i] based on linear OOA(32¹⁷, 524289, F₃₂, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(32¹⁷, 1048579, F₃₂, 5) (dual of [1048579, 1048562, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹⁷, 1048580, F₃₂, 5) (dual of [1048580, 1048563, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
32. digital (33, 43, 209760)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 6, 44)-net over F₃₂, using
      - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
    2. digital (27, 37, 209716)-net over F₃₂, using
      - net defined by OOA [i] based on linear OOA(32³⁷, 209716, F₃₂, 10, 10) (dual of [(209716, 10), 2097123, 11]-NRT-code), using
        OA 5-folding and stacking [i] based on linear OA(32³⁷, 1048580, F₃₂, 10) (dual of [1048580, 1048543, 11]-code), using
        constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
        linear OA(32³⁷, 1048576, F₃₂, 10) (dual of [1048576, 1048539, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(32³³, 1048576, F₃₂, 9) (dual of [1048576, 1048543, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code) (see above)

(72, 82, large)-Net in Base 32 — Constructive

(72, 82, large)-net in base 32, using

32² times duplication [i] based on (70, 80, large)-net in base 32, using
- base change [i] based on digital (40, 50, large)-net over F₂₅₆, using
  - 256¹ times duplication [i] based on digital (39, 49, large)-net over F₂₅₆, using
    - generalized (u,Â u+v)-construction [i] based on
      1. digital (0, 0, 32640)-net over F₂₅₆, using
        s-reduction based on digital (0, 0, s)-net over F₂₅₆ with arbitrarily large s, using
        arbitrary set of 256⁰ points [i]
      2. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      3. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      4. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      5. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      6. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      7. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      8. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      9. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      10. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      11. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      12. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      13. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      14. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      15. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      16. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      17. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      18. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      19. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      20. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      21. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      22. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      23. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      24. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      25. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      26. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      27. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      28. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      29. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      30. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      31. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      32. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      33. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      34. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      35. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      36. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      37. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      38. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      39. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      40. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      41. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      42. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      43. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      44. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      45. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      46. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      47. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      48. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      49. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      50. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      51. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      52. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      53. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      54. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      55. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      56. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      57. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      58. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      59. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      60. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      61. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      62. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      63. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      64. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      65. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      66. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      67. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      68. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      69. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      70. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      71. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      72. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      73. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      74. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      75. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      76. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      77. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      78. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      79. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      80. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      81. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      82. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      83. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      84. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      85. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      86. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      87. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      88. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      89. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      90. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      91. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      92. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      93. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      94. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      95. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      96. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      97. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      98. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      99. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      100. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      101. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      102. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      103. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      104. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      105. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      106. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      107. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      108. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      109. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      110. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      111. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      112. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      113. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      114. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      115. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      116. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      117. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      118. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      119. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      120. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      121. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      122. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      123. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      124. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      125. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      126. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      127. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      128. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      129. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      130. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      131. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      132. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      133. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      134. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      135. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      136. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      137. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      138. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      139. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      140. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      141. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      142. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      143. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      144. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      145. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      146. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      147. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      148. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      149. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      150. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      151. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      152. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      153. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      154. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      155. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      156. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      157. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      158. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      159. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      160. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      161. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      162. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      163. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      164. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      165. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      166. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      167. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      168. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      169. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      170. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      171. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      172. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      173. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      174. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      175. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      176. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      177. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      178. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      179. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      180. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      181. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      182. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      183. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      184. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      185. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      186. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      187. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      188. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      189. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      190. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      191. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      192. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      193. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      194. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      195. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      196. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      197. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      198. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      199. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      200. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      201. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      202. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      203. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      204. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      205. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      206. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      207. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      208. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      209. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      210. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      211. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      212. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      213. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      214. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      215. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      216. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      217. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      218. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      219. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      220. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      221. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      222. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      223. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      224. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      225. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      226. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      227. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      228. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      229. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      230. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      231. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      232. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      233. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      234. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      235. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      236. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      237. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      238. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      239. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      240. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      241. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      242. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      243. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      244. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      245. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      246. digital (0, 0, 32640)-net over F₂₅₆ (see above)
      247. digital (0, 1, 32640)-net over F₂₅₆, using
        s-reduction based on digital (0, 1, s)-net over F₂₅₆ with arbitrarily large s, using
        construction for strength kÂ =Â 1 [i]
      248. digital (0, 1, 32640)-net over F₂₅₆ (see above)
      249. digital (0, 1, 32640)-net over F₂₅₆ (see above)
      250. digital (0, 1, 32640)-net over F₂₅₆ (see above)
      251. digital (0, 1, 32640)-net over F₂₅₆ (see above)
      252. digital (1, 3, 32640)-net over F₂₅₆, using
        s-reduction based on digital (1, 3, 65793)-net over F₂₅₆, using
        kÂ =Â 2 construction [i]
      253. digital (1, 3, 32640)-net over F₂₅₆ (see above)
      254. digital (1, 4, 32640)-net over F₂₅₆, using
        s-reduction based on digital (1, 4, 65537)-net over F₂₅₆, using
        net defined by OOA [i] based on linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]
      255. digital (2, 7, 32640)-net over F₂₅₆, using
        net defined by OOA [i] based on linear OOA(256⁷, 32640, F₂₅₆, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
      256. digital (17, 27, 65792)-net over F₂₅₆, using
        generalized (u,Â u+v)-construction [i] based on
        digital (0, 0, 257)-net over F₂₅₆, using
        s-reduction based on digital (0, 0, s)-net over F₂₅₆ with arbitrarily large s (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 0, 257)-net over F₂₅₆ (see above)
        digital (0, 1, 257)-net over F₂₅₆, using
        s-reduction based on digital (0, 1, s)-net over F₂₅₆ with arbitrarily large s (see above)
        digital (0, 1, 257)-net over F₂₅₆ (see above)
        digital (0, 1, 257)-net over F₂₅₆ (see above)
        digital (0, 1, 257)-net over F₂₅₆ (see above)
        digital (0, 1, 257)-net over F₂₅₆ (see above)
        digital (0, 2, 257)-net over F₂₅₆, using
        kÂ =Â 2 construction [i]
        digital (0, 2, 257)-net over F₂₅₆ (see above)
        digital (0, 3, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
        digital (0, 5, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
        digital (0, 10, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(72, 82, large)-Net over F₃₂ — Digital

Digital (72, 82, large)-net over F₃₂, using

9 times m-reduction [i] based on digital (72, 91, large)-net over F₃₂, using
- Gilbertâ€“VarÅ¡amov bound [i]

(72, 82, large)-Net in Base 32 — Upper bound on s

There is no (72, 82, large)-net in base 32, because

8 times m-reduction [i] would yield (72, 74, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]

Best Known (72, 82, s)-Nets in Base 32

(72, 82, 6712320)-Net over F32 — Constructive and digital

(72, 82, large)-Net in Base 32 — Constructive

(72, 82, large)-Net over F32 — Digital

(72, 82, large)-Net in Base 32 — Upper bound on s

(72, 82, 6712320)-Net over F₃₂ — Constructive and digital

(72, 82, large)-Net over F₃₂ — Digital