Best Known (23, ∞, s)-Nets in Base 7
(23, ∞, 30)-Net over F7 — Constructive and digital
Digital (23, m, 30)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 29)-sequence over F7, using
(23, ∞, 72)-Net over F7 — Digital
Digital (23, m, 72)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 71)-sequence over F7, using
- t-expansion [i] based on digital (22, 71)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 22 and N(F) ≥ 72, using
- t-expansion [i] based on digital (22, 71)-sequence over F7, using
(23, ∞, 157)-Net in Base 7 — Upper bound on s
There is no (23, m, 158)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (23, 470, 158)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7470, 158, S7, 3, 447), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 172 771256 555050 793191 984040 370697 826297 870717 291717 107112 887574 213728 236056 310122 224933 820891 090779 492119 721325 241326 296987 872120 657823 503220 677148 257787 043251 615182 749335 399948 544700 921470 024164 413920 115950 258434 946654 494845 831977 591838 970671 308022 023282 960118 131338 149342 790794 517551 945945 395273 581519 480637 863680 389679 098785 615672 371113 477126 484763 355268 007230 787580 850079 816369 943157 267918 391739 / 8 > 7470 [i]
- extracting embedded OOA [i] would yield OOA(7470, 158, S7, 3, 447), but