Best Known (18, 18+∞, s)-Nets in Base 9
(18, 18+∞, 74)-Net over F9 — Constructive and digital
Digital (18, m, 74)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 73)-sequence over F9, using
- t-expansion [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- t-expansion [i] based on digital (17, 73)-sequence over F9, using
(18, 18+∞, 165)-Net in Base 9 — Upper bound on s
There is no (18, m, 166)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (18, 329, 166)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9329, 166, S9, 2, 311), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1323 966098 194879 734913 685231 457591 477025 608805 205501 491294 849010 567808 540034 210857 358751 636824 493038 809511 105055 135196 821714 846579 767851 571854 117965 566648 469064 583921 076669 218550 625765 413077 307877 812704 629502 215924 634619 054639 625248 972916 253829 222437 839671 595142 592990 882815 958374 890719 964691 764550 031931 842303 275335 / 13 > 9329 [i]
- extracting embedded OOA [i] would yield OOA(9329, 166, S9, 2, 311), but