Best Known (56−42, 56, s)-Nets in Base 5
(56−42, 56, 35)-Net over F5 — Constructive and digital
Digital (14, 56, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 3 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(56−42, 56, 39)-Net over F5 — Digital
Digital (14, 56, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(56−42, 56, 127)-Net in Base 5 — Upper bound on s
There is no (14, 56, 128)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(556, 128, S5, 42), but
- the linear programming bound shows that M ≥ 549735 398501 526414 075158 979671 639898 292285 145479 291111 849918 866537 987237 449983 859460 265513 853090 822065 634239 233128 311909 739703 061552 607010 753490 612842 142581 939697 265625 / 377 513813 859449 872268 885907 623007 915455 565045 525435 446662 093459 644502 790412 571230 762657 343613 222871 542428 531126 548885 770756 807129 > 556 [i]