MinT - Best Known (40, 48, s)-Nets in Base 64

Best Known (40, 48, s)-Nets in Base 64

(40, 48, 6291450)-Net over F₆₄ — Constructive and digital

Digital (40, 48, 6291450)-net over F₆₄, using

64¹ times duplication [i] based on digital (39, 47, 6291450)-net over F₆₄, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (3, 5, 2097150)-net over F₆₄, using
    - s-reduction based on digital (3, 5, large)-net over F₆₄, using
      - kÂ =Â 2 construction [i]
  2. 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]
  3. digital (21, 29, 2097150)-net over F₆₄, using
    - net defined by OOA [i] based on linear OOA(64²⁹, 2097150, F₆₄, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
      - OA 4-folding and stacking [i] based on linear OA(64²⁹, 8388600, F₆₄, 8) (dual of [8388600, 8388571, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(64²⁹, large, F₆₄, 8) (dual of [large, large−29, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

(40, 48, large)-Net in Base 64 — Constructive

(40, 48, large)-net in base 64, using

base change [i] based on digital (28, 36, 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, 0, 32640)-net over F₂₅₆ (see above)
  249. 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]
  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, 3, 32640)-net over F₂₅₆ (see above)
  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 (12, 20, 65792)-net over F₂₅₆, using
    - generalized (u,Â u+v)-construction [i] based on
      1. 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)
      2. digital (0, 0, 257)-net over F₂₅₆ (see above)
      3. digital (0, 0, 257)-net over F₂₅₆ (see above)
      4. digital (0, 0, 257)-net over F₂₅₆ (see above)
      5. digital (0, 0, 257)-net over F₂₅₆ (see above)
      6. digital (0, 0, 257)-net over F₂₅₆ (see above)
      7. digital (0, 0, 257)-net over F₂₅₆ (see above)
      8. digital (0, 0, 257)-net over F₂₅₆ (see above)
      9. digital (0, 0, 257)-net over F₂₅₆ (see above)
      10. digital (0, 0, 257)-net over F₂₅₆ (see above)
      11. digital (0, 0, 257)-net over F₂₅₆ (see above)
      12. digital (0, 0, 257)-net over F₂₅₆ (see above)
      13. digital (0, 0, 257)-net over F₂₅₆ (see above)
      14. digital (0, 0, 257)-net over F₂₅₆ (see above)
      15. digital (0, 0, 257)-net over F₂₅₆ (see above)
      16. digital (0, 0, 257)-net over F₂₅₆ (see above)
      17. digital (0, 0, 257)-net over F₂₅₆ (see above)
      18. digital (0, 0, 257)-net over F₂₅₆ (see above)
      19. digital (0, 0, 257)-net over F₂₅₆ (see above)
      20. digital (0, 0, 257)-net over F₂₅₆ (see above)
      21. digital (0, 0, 257)-net over F₂₅₆ (see above)
      22. digital (0, 0, 257)-net over F₂₅₆ (see above)
      23. digital (0, 0, 257)-net over F₂₅₆ (see above)
      24. digital (0, 0, 257)-net over F₂₅₆ (see above)
      25. digital (0, 0, 257)-net over F₂₅₆ (see above)
      26. digital (0, 0, 257)-net over F₂₅₆ (see above)
      27. digital (0, 0, 257)-net over F₂₅₆ (see above)
      28. digital (0, 0, 257)-net over F₂₅₆ (see above)
      29. digital (0, 0, 257)-net over F₂₅₆ (see above)
      30. digital (0, 0, 257)-net over F₂₅₆ (see above)
      31. digital (0, 0, 257)-net over F₂₅₆ (see above)
      32. digital (0, 0, 257)-net over F₂₅₆ (see above)
      33. digital (0, 0, 257)-net over F₂₅₆ (see above)
      34. digital (0, 0, 257)-net over F₂₅₆ (see above)
      35. digital (0, 0, 257)-net over F₂₅₆ (see above)
      36. digital (0, 0, 257)-net over F₂₅₆ (see above)
      37. digital (0, 0, 257)-net over F₂₅₆ (see above)
      38. digital (0, 0, 257)-net over F₂₅₆ (see above)
      39. digital (0, 0, 257)-net over F₂₅₆ (see above)
      40. digital (0, 0, 257)-net over F₂₅₆ (see above)
      41. digital (0, 0, 257)-net over F₂₅₆ (see above)
      42. digital (0, 0, 257)-net over F₂₅₆ (see above)
      43. digital (0, 0, 257)-net over F₂₅₆ (see above)
      44. digital (0, 0, 257)-net over F₂₅₆ (see above)
      45. digital (0, 0, 257)-net over F₂₅₆ (see above)
      46. digital (0, 0, 257)-net over F₂₅₆ (see above)
      47. digital (0, 0, 257)-net over F₂₅₆ (see above)
      48. digital (0, 0, 257)-net over F₂₅₆ (see above)
      49. digital (0, 0, 257)-net over F₂₅₆ (see above)
      50. digital (0, 0, 257)-net over F₂₅₆ (see above)
      51. digital (0, 0, 257)-net over F₂₅₆ (see above)
      52. digital (0, 0, 257)-net over F₂₅₆ (see above)
      53. digital (0, 0, 257)-net over F₂₅₆ (see above)
      54. digital (0, 0, 257)-net over F₂₅₆ (see above)
      55. digital (0, 0, 257)-net over F₂₅₆ (see above)
      56. digital (0, 0, 257)-net over F₂₅₆ (see above)
      57. digital (0, 0, 257)-net over F₂₅₆ (see above)
      58. digital (0, 0, 257)-net over F₂₅₆ (see above)
      59. digital (0, 0, 257)-net over F₂₅₆ (see above)
      60. digital (0, 0, 257)-net over F₂₅₆ (see above)
      61. digital (0, 0, 257)-net over F₂₅₆ (see above)
      62. digital (0, 0, 257)-net over F₂₅₆ (see above)
      63. digital (0, 0, 257)-net over F₂₅₆ (see above)
      64. digital (0, 0, 257)-net over F₂₅₆ (see above)
      65. digital (0, 0, 257)-net over F₂₅₆ (see above)
      66. digital (0, 0, 257)-net over F₂₅₆ (see above)
      67. digital (0, 0, 257)-net over F₂₅₆ (see above)
      68. digital (0, 0, 257)-net over F₂₅₆ (see above)
      69. digital (0, 0, 257)-net over F₂₅₆ (see above)
      70. digital (0, 0, 257)-net over F₂₅₆ (see above)
      71. digital (0, 0, 257)-net over F₂₅₆ (see above)
      72. digital (0, 0, 257)-net over F₂₅₆ (see above)
      73. digital (0, 0, 257)-net over F₂₅₆ (see above)
      74. digital (0, 0, 257)-net over F₂₅₆ (see above)
      75. digital (0, 0, 257)-net over F₂₅₆ (see above)
      76. digital (0, 0, 257)-net over F₂₅₆ (see above)
      77. digital (0, 0, 257)-net over F₂₅₆ (see above)
      78. digital (0, 0, 257)-net over F₂₅₆ (see above)
      79. digital (0, 0, 257)-net over F₂₅₆ (see above)
      80. digital (0, 0, 257)-net over F₂₅₆ (see above)
      81. digital (0, 0, 257)-net over F₂₅₆ (see above)
      82. digital (0, 0, 257)-net over F₂₅₆ (see above)
      83. digital (0, 0, 257)-net over F₂₅₆ (see above)
      84. digital (0, 0, 257)-net over F₂₅₆ (see above)
      85. digital (0, 0, 257)-net over F₂₅₆ (see above)
      86. digital (0, 0, 257)-net over F₂₅₆ (see above)
      87. digital (0, 0, 257)-net over F₂₅₆ (see above)
      88. digital (0, 0, 257)-net over F₂₅₆ (see above)
      89. digital (0, 0, 257)-net over F₂₅₆ (see above)
      90. digital (0, 0, 257)-net over F₂₅₆ (see above)
      91. digital (0, 0, 257)-net over F₂₅₆ (see above)
      92. digital (0, 0, 257)-net over F₂₅₆ (see above)
      93. digital (0, 0, 257)-net over F₂₅₆ (see above)
      94. digital (0, 0, 257)-net over F₂₅₆ (see above)
      95. digital (0, 0, 257)-net over F₂₅₆ (see above)
      96. digital (0, 0, 257)-net over F₂₅₆ (see above)
      97. digital (0, 0, 257)-net over F₂₅₆ (see above)
      98. digital (0, 0, 257)-net over F₂₅₆ (see above)
      99. digital (0, 0, 257)-net over F₂₅₆ (see above)
      100. digital (0, 0, 257)-net over F₂₅₆ (see above)
      101. digital (0, 0, 257)-net over F₂₅₆ (see above)
      102. digital (0, 0, 257)-net over F₂₅₆ (see above)
      103. digital (0, 0, 257)-net over F₂₅₆ (see above)
      104. digital (0, 0, 257)-net over F₂₅₆ (see above)
      105. digital (0, 0, 257)-net over F₂₅₆ (see above)
      106. digital (0, 0, 257)-net over F₂₅₆ (see above)
      107. digital (0, 0, 257)-net over F₂₅₆ (see above)
      108. digital (0, 0, 257)-net over F₂₅₆ (see above)
      109. digital (0, 0, 257)-net over F₂₅₆ (see above)
      110. digital (0, 0, 257)-net over F₂₅₆ (see above)
      111. digital (0, 0, 257)-net over F₂₅₆ (see above)
      112. digital (0, 0, 257)-net over F₂₅₆ (see above)
      113. digital (0, 0, 257)-net over F₂₅₆ (see above)
      114. digital (0, 0, 257)-net over F₂₅₆ (see above)
      115. digital (0, 0, 257)-net over F₂₅₆ (see above)
      116. digital (0, 0, 257)-net over F₂₅₆ (see above)
      117. digital (0, 0, 257)-net over F₂₅₆ (see above)
      118. digital (0, 0, 257)-net over F₂₅₆ (see above)
      119. digital (0, 0, 257)-net over F₂₅₆ (see above)
      120. digital (0, 0, 257)-net over F₂₅₆ (see above)
      121. digital (0, 0, 257)-net over F₂₅₆ (see above)
      122. digital (0, 0, 257)-net over F₂₅₆ (see above)
      123. digital (0, 0, 257)-net over F₂₅₆ (see above)
      124. digital (0, 0, 257)-net over F₂₅₆ (see above)
      125. digital (0, 0, 257)-net over F₂₅₆ (see above)
      126. digital (0, 0, 257)-net over F₂₅₆ (see above)
      127. digital (0, 0, 257)-net over F₂₅₆ (see above)
      128. digital (0, 0, 257)-net over F₂₅₆ (see above)
      129. digital (0, 0, 257)-net over F₂₅₆ (see above)
      130. digital (0, 0, 257)-net over F₂₅₆ (see above)
      131. digital (0, 0, 257)-net over F₂₅₆ (see above)
      132. digital (0, 0, 257)-net over F₂₅₆ (see above)
      133. digital (0, 0, 257)-net over F₂₅₆ (see above)
      134. digital (0, 0, 257)-net over F₂₅₆ (see above)
      135. digital (0, 0, 257)-net over F₂₅₆ (see above)
      136. digital (0, 0, 257)-net over F₂₅₆ (see above)
      137. digital (0, 0, 257)-net over F₂₅₆ (see above)
      138. digital (0, 0, 257)-net over F₂₅₆ (see above)
      139. digital (0, 0, 257)-net over F₂₅₆ (see above)
      140. digital (0, 0, 257)-net over F₂₅₆ (see above)
      141. digital (0, 0, 257)-net over F₂₅₆ (see above)
      142. digital (0, 0, 257)-net over F₂₅₆ (see above)
      143. digital (0, 0, 257)-net over F₂₅₆ (see above)
      144. digital (0, 0, 257)-net over F₂₅₆ (see above)
      145. digital (0, 0, 257)-net over F₂₅₆ (see above)
      146. digital (0, 0, 257)-net over F₂₅₆ (see above)
      147. digital (0, 0, 257)-net over F₂₅₆ (see above)
      148. digital (0, 0, 257)-net over F₂₅₆ (see above)
      149. digital (0, 0, 257)-net over F₂₅₆ (see above)
      150. digital (0, 0, 257)-net over F₂₅₆ (see above)
      151. digital (0, 0, 257)-net over F₂₅₆ (see above)
      152. digital (0, 0, 257)-net over F₂₅₆ (see above)
      153. digital (0, 0, 257)-net over F₂₅₆ (see above)
      154. digital (0, 0, 257)-net over F₂₅₆ (see above)
      155. digital (0, 0, 257)-net over F₂₅₆ (see above)
      156. digital (0, 0, 257)-net over F₂₅₆ (see above)
      157. digital (0, 0, 257)-net over F₂₅₆ (see above)
      158. digital (0, 0, 257)-net over F₂₅₆ (see above)
      159. digital (0, 0, 257)-net over F₂₅₆ (see above)
      160. digital (0, 0, 257)-net over F₂₅₆ (see above)
      161. digital (0, 0, 257)-net over F₂₅₆ (see above)
      162. digital (0, 0, 257)-net over F₂₅₆ (see above)
      163. digital (0, 0, 257)-net over F₂₅₆ (see above)
      164. digital (0, 0, 257)-net over F₂₅₆ (see above)
      165. digital (0, 0, 257)-net over F₂₅₆ (see above)
      166. digital (0, 0, 257)-net over F₂₅₆ (see above)
      167. digital (0, 0, 257)-net over F₂₅₆ (see above)
      168. digital (0, 0, 257)-net over F₂₅₆ (see above)
      169. digital (0, 0, 257)-net over F₂₅₆ (see above)
      170. digital (0, 0, 257)-net over F₂₅₆ (see above)
      171. digital (0, 0, 257)-net over F₂₅₆ (see above)
      172. digital (0, 0, 257)-net over F₂₅₆ (see above)
      173. digital (0, 0, 257)-net over F₂₅₆ (see above)
      174. digital (0, 0, 257)-net over F₂₅₆ (see above)
      175. digital (0, 0, 257)-net over F₂₅₆ (see above)
      176. digital (0, 0, 257)-net over F₂₅₆ (see above)
      177. digital (0, 0, 257)-net over F₂₅₆ (see above)
      178. digital (0, 0, 257)-net over F₂₅₆ (see above)
      179. digital (0, 0, 257)-net over F₂₅₆ (see above)
      180. digital (0, 0, 257)-net over F₂₅₆ (see above)
      181. digital (0, 0, 257)-net over F₂₅₆ (see above)
      182. digital (0, 0, 257)-net over F₂₅₆ (see above)
      183. digital (0, 0, 257)-net over F₂₅₆ (see above)
      184. digital (0, 0, 257)-net over F₂₅₆ (see above)
      185. digital (0, 0, 257)-net over F₂₅₆ (see above)
      186. digital (0, 0, 257)-net over F₂₅₆ (see above)
      187. digital (0, 0, 257)-net over F₂₅₆ (see above)
      188. digital (0, 0, 257)-net over F₂₅₆ (see above)
      189. digital (0, 0, 257)-net over F₂₅₆ (see above)
      190. digital (0, 0, 257)-net over F₂₅₆ (see above)
      191. digital (0, 0, 257)-net over F₂₅₆ (see above)
      192. digital (0, 0, 257)-net over F₂₅₆ (see above)
      193. digital (0, 0, 257)-net over F₂₅₆ (see above)
      194. digital (0, 0, 257)-net over F₂₅₆ (see above)
      195. digital (0, 0, 257)-net over F₂₅₆ (see above)
      196. digital (0, 0, 257)-net over F₂₅₆ (see above)
      197. digital (0, 0, 257)-net over F₂₅₆ (see above)
      198. digital (0, 0, 257)-net over F₂₅₆ (see above)
      199. digital (0, 0, 257)-net over F₂₅₆ (see above)
      200. digital (0, 0, 257)-net over F₂₅₆ (see above)
      201. digital (0, 0, 257)-net over F₂₅₆ (see above)
      202. digital (0, 0, 257)-net over F₂₅₆ (see above)
      203. digital (0, 0, 257)-net over F₂₅₆ (see above)
      204. digital (0, 0, 257)-net over F₂₅₆ (see above)
      205. digital (0, 0, 257)-net over F₂₅₆ (see above)
      206. digital (0, 0, 257)-net over F₂₅₆ (see above)
      207. digital (0, 0, 257)-net over F₂₅₆ (see above)
      208. digital (0, 0, 257)-net over F₂₅₆ (see above)
      209. digital (0, 0, 257)-net over F₂₅₆ (see above)
      210. digital (0, 0, 257)-net over F₂₅₆ (see above)
      211. digital (0, 0, 257)-net over F₂₅₆ (see above)
      212. digital (0, 0, 257)-net over F₂₅₆ (see above)
      213. digital (0, 0, 257)-net over F₂₅₆ (see above)
      214. digital (0, 0, 257)-net over F₂₅₆ (see above)
      215. digital (0, 0, 257)-net over F₂₅₆ (see above)
      216. digital (0, 0, 257)-net over F₂₅₆ (see above)
      217. digital (0, 0, 257)-net over F₂₅₆ (see above)
      218. digital (0, 0, 257)-net over F₂₅₆ (see above)
      219. digital (0, 0, 257)-net over F₂₅₆ (see above)
      220. digital (0, 0, 257)-net over F₂₅₆ (see above)
      221. digital (0, 0, 257)-net over F₂₅₆ (see above)
      222. digital (0, 0, 257)-net over F₂₅₆ (see above)
      223. digital (0, 0, 257)-net over F₂₅₆ (see above)
      224. digital (0, 0, 257)-net over F₂₅₆ (see above)
      225. digital (0, 0, 257)-net over F₂₅₆ (see above)
      226. digital (0, 0, 257)-net over F₂₅₆ (see above)
      227. digital (0, 0, 257)-net over F₂₅₆ (see above)
      228. digital (0, 0, 257)-net over F₂₅₆ (see above)
      229. digital (0, 0, 257)-net over F₂₅₆ (see above)
      230. digital (0, 0, 257)-net over F₂₅₆ (see above)
      231. digital (0, 0, 257)-net over F₂₅₆ (see above)
      232. digital (0, 0, 257)-net over F₂₅₆ (see above)
      233. digital (0, 0, 257)-net over F₂₅₆ (see above)
      234. digital (0, 0, 257)-net over F₂₅₆ (see above)
      235. digital (0, 0, 257)-net over F₂₅₆ (see above)
      236. digital (0, 0, 257)-net over F₂₅₆ (see above)
      237. digital (0, 0, 257)-net over F₂₅₆ (see above)
      238. digital (0, 0, 257)-net over F₂₅₆ (see above)
      239. digital (0, 0, 257)-net over F₂₅₆ (see above)
      240. digital (0, 0, 257)-net over F₂₅₆ (see above)
      241. digital (0, 0, 257)-net over F₂₅₆ (see above)
      242. digital (0, 0, 257)-net over F₂₅₆ (see above)
      243. digital (0, 0, 257)-net over F₂₅₆ (see above)
      244. digital (0, 0, 257)-net over F₂₅₆ (see above)
      245. digital (0, 0, 257)-net over F₂₅₆ (see above)
      246. digital (0, 0, 257)-net over F₂₅₆ (see above)
      247. digital (0, 0, 257)-net over F₂₅₆ (see above)
      248. digital (0, 0, 257)-net over F₂₅₆ (see above)
      249. 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)
      250. digital (0, 1, 257)-net over F₂₅₆ (see above)
      251. digital (0, 1, 257)-net over F₂₅₆ (see above)
      252. digital (0, 1, 257)-net over F₂₅₆ (see above)
      253. digital (0, 2, 257)-net over F₂₅₆, using
        kÂ =Â 2 construction [i]
      254. digital (0, 2, 257)-net over F₂₅₆ (see above)
      255. digital (0, 4, 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]
      256. digital (0, 8, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(40, 48, large)-Net over F₆₄ — Digital

Digital (40, 48, large)-net over F₆₄, using

t-expansion [i] based on digital (37, 48, large)-net over F₆₄, using
- 2 times m-reduction [i] based on digital (37, 50, large)-net over F₆₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(64⁵⁰, large, F₆₄, 13) (dual of [large, large−50, 14]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

(40, 48, large)-Net in Base 64 — Upper bound on s

There is no (40, 48, large)-net in base 64, because

6 times m-reduction [i] would yield (40, 42, large)-net in base 64, but
- mutually orthogonal hypercube bound [i]

Best Known (40, 48, s)-Nets in Base 64

(40, 48, 6291450)-Net over F64 — Constructive and digital

(40, 48, large)-Net in Base 64 — Constructive

(40, 48, large)-Net over F64 — Digital

(40, 48, large)-Net in Base 64 — Upper bound on s

(40, 48, 6291450)-Net over F₆₄ — Constructive and digital

(40, 48, large)-Net over F₆₄ — Digital