Best Known (94, ∞, s)-Nets in Base 3
(94, ∞, 64)-Net over F3 — Constructive and digital
Digital (94, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, ∞, 96)-Net over F3 — Digital
Digital (94, m, 96)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, ∞, 201)-Net in Base 3 — Upper bound on s
There is no (94, m, 202)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (94, 1003, 202)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31003, 202, S3, 5, 909), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22 809687 848502 356906 271024 596503 746746 001426 331072 812336 722871 113017 473790 022699 631777 048248 864540 893063 335394 604142 663387 221819 404981 978086 412758 038875 474737 998531 745346 628829 307388 899772 330406 507057 573228 756427 063597 736662 945248 339876 201183 702157 394984 703091 198912 382028 903329 512112 069538 729998 502068 098217 984623 530871 880253 310868 120005 989885 535853 639676 761370 574516 547190 865248 022313 750746 871781 966645 619531 325101 334722 365855 987203 597834 852099 679129 658878 382542 071880 961110 677253 / 455 > 31003 [i]
- extracting embedded OOA [i] would yield OOA(31003, 202, S3, 5, 909), but