Best Known (24, 24+∞, s)-Nets in Base 9
(24, 24+∞, 78)-Net over F9 — Constructive and digital
Digital (24, m, 78)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (24, 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
(24, 24+∞, 92)-Net over F9 — Digital
Digital (24, m, 92)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (24, 91)-sequence over F9, using
- t-expansion [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
- t-expansion [i] based on digital (23, 91)-sequence over F9, using
(24, 24+∞, 215)-Net in Base 9 — Upper bound on s
There is no (24, m, 216)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (24, 429, 216)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9429, 216, S9, 2, 405), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5696 955446 943115 756721 736431 699869 003572 428786 945238 403575 277867 834976 569574 342633 907659 907726 760813 501100 049111 102654 684811 345649 855787 384766 334717 198188 753379 666108 338753 389725 177294 575220 185541 496352 681776 439974 231330 876953 961038 611936 188437 626075 253533 887345 134755 788522 107584 697563 284106 766808 557311 172369 561039 252785 197869 586862 687567 848411 361768 006906 702969 938222 949927 423898 249207 237001 401960 826444 848427 / 203 > 9429 [i]
- extracting embedded OOA [i] would yield OOA(9429, 216, S9, 2, 405), but