Best Known (23, 23+∞, s)-Nets in Base 9
(23, 23+∞, 78)-Net over F9 — Constructive and digital
Digital (23, m, 78)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 77)-sequence over F9, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- t-expansion [i] based on digital (22, 77)-sequence over F9, using
(23, 23+∞, 92)-Net over F9 — Digital
Digital (23, m, 92)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (23, 91)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 23 and N(F) ≥ 92, using
(23, 23+∞, 206)-Net in Base 9 — Upper bound on s
There is no (23, m, 207)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (23, 411, 207)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9411, 207, S9, 2, 388), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 63259 594362 697567 486884 711016 198836 637103 274227 399681 813182 752993 558566 774734 429353 388742 507806 579005 225228 820578 588464 575331 139251 890375 692223 678479 337045 448358 126544 619718 348026 264867 233001 979636 229487 214787 362874 848701 193429 317456 370567 279485 788814 574102 103350 224869 273989 959608 578587 593118 169122 775441 476343 382958 982610 960512 325628 797369 468049 353846 360212 417294 450493 007130 991474 905998 661645 / 389 > 9411 [i]
- extracting embedded OOA [i] would yield OOA(9411, 207, S9, 2, 388), but