Best Known (97, 97+∞, s)-Nets in Base 3
(97, 97+∞, 64)-Net over F3 — Constructive and digital
Digital (97, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (97, 63)-sequence over F3, using
- t-expansion [i] based on digital (89, 63)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- t-expansion [i] based on digital (89, 63)-sequence over F3, using
(97, 97+∞, 96)-Net over F3 — Digital
Digital (97, m, 96)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (97, 95)-sequence over F3, using
- t-expansion [i] based on digital (89, 95)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 89 and N(F) ≥ 96, using
- t-expansion [i] based on digital (89, 95)-sequence over F3, using
(97, 97+∞, 207)-Net in Base 3 — Upper bound on s
There is no (97, m, 208)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (97, 1033, 208)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31033, 208, S3, 5, 936), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9194 189170 220641 393590 917798 867532 049106 966536 179229 829669 289195 584187 877343 509556 889917 190007 480833 221738 865181 392544 646854 647344 037415 226500 379695 656624 175615 450470 663668 846153 791755 716661 739846 690528 221904 206587 056501 510488 288618 112363 225709 065333 517180 311265 018526 525704 475460 669425 057782 236873 480706 181493 365707 862977 826486 758353 696687 310979 611597 321517 771991 946535 228364 584342 650662 707182 420663 310736 611147 263923 111426 445031 145393 978411 775844 940034 488796 936970 650906 606862 847060 604216 019273 / 937 > 31033 [i]
- extracting embedded OOA [i] would yield OOA(31033, 208, S3, 5, 936), but