Best Known (58−43, 58, s)-Nets in Base 5
(58−43, 58, 36)-Net over F5 — Constructive and digital
Digital (15, 58, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-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 4 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]
(58−43, 58, 39)-Net over F5 — Digital
Digital (15, 58, 39)-net over F5, using
- t-expansion [i] based on digital (14, 58, 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
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(58−43, 58, 140)-Net in Base 5 — Upper bound on s
There is no (15, 58, 141)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(558, 141, S5, 43), but
- the linear programming bound shows that M ≥ 1591 576286 023843 781170 746136 002297 993825 547570 593206 378640 998725 013830 463633 279691 813374 538867 398050 378199 059196 049347 519874 572753 906250 000000 / 45454 293771 604069 763210 603226 553233 374660 739934 352611 432932 184144 831489 178003 786054 826732 574131 319969 > 558 [i]