Best Known (15, 65, s)-Nets in Base 5
(15, 65, 36)-Net over F5 — Constructive and digital
Digital (15, 65, 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]
(15, 65, 39)-Net over F5 — Digital
Digital (15, 65, 39)-net over F5, using
- t-expansion [i] based on digital (14, 65, 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
(15, 65, 106)-Net in Base 5 — Upper bound on s
There is no (15, 65, 107)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(565, 107, S5, 50), but
- the linear programming bound shows that M ≥ 3 460864 699839 516032 970167 850868 074536 364440 760410 066537 478370 775338 110121 310819 522477 686405 181884 765625 / 1198 473810 511228 830549 728619 203929 079038 354841 407181 660217 > 565 [i]