MinT - Best Known (77, 77+11, s)-Nets in Base 32

Best Known (77, 77+11, s)-Nets in Base 32

(77, 77+11, 6726752)-Net over F₃₂ — Constructive and digital

Digital (77, 88, 6726752)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 0, 210211)-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, 210211)-net over F₃₂ (see above)
3. digital (0, 0, 210211)-net over F₃₂ (see above)
4. digital (0, 0, 210211)-net over F₃₂ (see above)
5. digital (0, 0, 210211)-net over F₃₂ (see above)
6. digital (0, 0, 210211)-net over F₃₂ (see above)
7. digital (0, 0, 210211)-net over F₃₂ (see above)
8. digital (0, 0, 210211)-net over F₃₂ (see above)
9. digital (0, 0, 210211)-net over F₃₂ (see above)
10. digital (0, 0, 210211)-net over F₃₂ (see above)
11. digital (0, 0, 210211)-net over F₃₂ (see above)
12. digital (0, 0, 210211)-net over F₃₂ (see above)
13. digital (0, 0, 210211)-net over F₃₂ (see above)
14. digital (0, 0, 210211)-net over F₃₂ (see above)
15. digital (0, 0, 210211)-net over F₃₂ (see above)
16. digital (0, 0, 210211)-net over F₃₂ (see above)
17. digital (0, 0, 210211)-net over F₃₂ (see above)
18. digital (0, 0, 210211)-net over F₃₂ (see above)
19. digital (0, 0, 210211)-net over F₃₂ (see above)
20. digital (0, 0, 210211)-net over F₃₂ (see above)
21. digital (0, 0, 210211)-net over F₃₂ (see above)
22. digital (0, 1, 210211)-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]
23. digital (0, 1, 210211)-net over F₃₂ (see above)
24. digital (0, 1, 210211)-net over F₃₂ (see above)
25. digital (0, 1, 210211)-net over F₃₂ (see above)
26. digital (0, 1, 210211)-net over F₃₂ (see above)
27. digital (0, 1, 210211)-net over F₃₂ (see above)
28. digital (3, 5, 210211)-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, 210211)-net over F₃₂ (see above)
30. digital (4, 7, 210211)-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, 210211)-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 (37, 48, 210211)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (2, 7, 496)-net over F₃₂, using
      - net defined by OOA [i] based on linear OOA(32⁷, 496, F₃₂, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
        a code by Danev and Olsson [i]
    2. digital (30, 41, 209715)-net over F₃₂, using
      - net defined by OOA [i] based on linear OOA(32⁴¹, 209715, F₃₂, 11, 11) (dual of [(209715, 11), 2306824, 12]-NRT-code), using
        OOA 5-folding and stacking with additional row [i] based on linear OA(32⁴¹, 1048576, F₃₂, 11) (dual of [1048576, 1048535, 12]-code), using
        an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(77, 77+11, large)-Net in Base 32 — Constructive

(77, 88, large)-net in base 32, using

base change [i] based on digital (44, 55, large)-net over F₂₅₆, using
- 256³ times duplication [i] based on digital (41, 52, 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, 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]
    247. digital (0, 1, 32640)-net over F₂₅₆ (see above)
    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 (18, 29, 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, 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, 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, 11, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(77, 77+11, large)-Net over F₃₂ — Digital

Digital (77, 88, large)-net over F₃₂, using

t-expansion [i] based on digital (75, 88, large)-net over F₃₂, using
- 7 times m-reduction [i] based on digital (75, 95, large)-net over F₃₂, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+11, large)-Net in Base 32 — Upper bound on s

There is no (77, 88, large)-net in base 32, because

9 times m-reduction [i] would yield (77, 79, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]

Best Known (77, 77+11, s)-Nets in Base 32

(77, 77+11, 6726752)-Net over F32 — Constructive and digital

(77, 77+11, large)-Net in Base 32 — Constructive

(77, 77+11, large)-Net over F32 — Digital

(77, 77+11, large)-Net in Base 32 — Upper bound on s

(77, 77+11, 6726752)-Net over F₃₂ — Constructive and digital

(77, 77+11, large)-Net over F₃₂ — Digital