Best Known (69−57, 69, s)-Nets in Base 7
(69−57, 69, 20)-Net over F7 — Constructive and digital
Digital (12, 69, 20)-net over F7, using
- net from sequence [i] based on digital (12, 19)-sequence over F7, using
(69−57, 69, 38)-Net over F7 — Digital
Digital (12, 69, 38)-net over F7, using
- t-expansion [i] based on digital (9, 69, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(69−57, 69, 139)-Net in Base 7 — Upper bound on s
There is no (12, 69, 140)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(769, 140, S7, 57), but
- the linear programming bound shows that M ≥ 14 736169 117025 764450 441945 811443 681105 435838 509115 644314 077572 338776 577347 829137 239756 632557 490542 707399 062333 987197 690531 614274 808720 418166 998380 387158 276334 784134 938437 197867 407709 132796 610551 535820 431345 / 662 170927 179722 618799 307135 202622 532316 399090 358699 652075 129350 736123 923168 126389 205537 429763 988708 568401 967277 252655 294021 317558 557808 867102 807097 > 769 [i]