MinT - Best Known (48, 57, s)-Nets in Base 64

Best Known (48, 57, s)-Nets in Base 64

(48, 57, 6557755)-Net over F₆₄ — Constructive and digital

Digital (48, 57, 6557755)-net over F₆₄, using

generalized (u,Â u+v)-construction [i] based on
1. digital (2, 4, 266305)-net over F₆₄, using
  - kÂ =Â 2 construction [i]
2. digital (4, 7, 2097150)-net over F₆₄, using
  - s-reduction based on digital (4, 7, large)-net over F₆₄, using
    - net defined by OOA [i] based on linear OOA(64⁷, large, F₆₄, 3, 3), using
      - appending kth column [i] based on linear OOA(64⁷, large, F₆₄, 2, 3), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁷, large, F₆₄, 3) (dual of [large, large−7, 4]-code), using
        product of projective cap with 64²-ovoid cap in AG(3,Â 64) [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
        ovoid in PG(3,Â 64) [i]
3. digital (9, 13, 2097150)-net over F₆₄, using
  - s-reduction based on digital (9, 13, 4194301)-net over F₆₄, using
    - net defined by OOA [i] based on linear OOA(64¹³, 4194301, F₆₄, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(64¹³, 4194301, F₆₄, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(64¹³, 8388602, F₆₄, 4) (dual of [8388602, 8388589, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹³, large, F₆₄, 4) (dual of [large, large−13, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
4. digital (24, 33, 2097150)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64³³, 2097150, F₆₄, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
    - OOA 4-folding and stacking with additional row [i] based on linear OA(64³³, 8388601, F₆₄, 9) (dual of [8388601, 8388568, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

(48, 57, large)-Net in Base 64 — Constructive

(48, 57, large)-net in base 64, using

64¹ times duplication [i] based on (47, 56, large)-net in base 64, using
- base change [i] based on digital (33, 42, large)-net over F₂₅₆, using
  - 256¹ times duplication [i] based on digital (32, 41, 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, 0, 32640)-net over F₂₅₆ (see above)
      248. 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]
      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 (0, 1, 32640)-net over F₂₅₆ (see above)
      253. 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]
      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, 6, 32640)-net over F₂₅₆, using
        net defined by OOA [i] based on linear OOA(256⁶, 32640, F₂₅₆, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(256⁶, 65280, F₂₅₆, 4) (dual of [65280, 65274, 5]-code), using
        1 times truncation [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 (14, 23, 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, 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, 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, 4, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
        digital (0, 9, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(48, 57, large)-Net over F₆₄ — Digital

Digital (48, 57, large)-net over F₆₄, using

t-expansion [i] based on digital (47, 57, large)-net over F₆₄, using
- 6 times m-reduction [i] based on digital (47, 63, large)-net over F₆₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(64⁶³, large, F₆₄, 16) (dual of [large, large−63, 17]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(64⁶¹, large, F₆₄, 16) (dual of [large, large−61, 17]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

(48, 57, large)-Net in Base 64 — Upper bound on s

There is no (48, 57, large)-net in base 64, because

7 times m-reduction [i] would yield (48, 50, large)-net in base 64, but
- mutually orthogonal hypercube bound [i]

Best Known (48, 57, s)-Nets in Base 64

(48, 57, 6557755)-Net over F64 — Constructive and digital

(48, 57, large)-Net in Base 64 — Constructive

(48, 57, large)-Net over F64 — Digital

(48, 57, large)-Net in Base 64 — Upper bound on s

(48, 57, 6557755)-Net over F₆₄ — Constructive and digital

(48, 57, large)-Net over F₆₄ — Digital