Best Known (3, 3+58, s)-Nets in Base 25
(3, 3+58, 52)-Net over F25 — Constructive and digital
Digital (3, 61, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(3, 3+58, 56)-Net over F25 — Digital
Digital (3, 61, 56)-net over F25, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(3, 3+58, 246)-Net in Base 25 — Upper bound on s
There is no (3, 61, 247)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2561, 247, S25, 58), but
- the linear programming bound shows that M ≥ 43 933086 245125 709578 087811 793942 952407 678412 216248 520607 078664 745870 355545 775964 856147 766113 281250 000000 000000 000000 / 2 310032 144994 652742 234456 994723 > 2561 [i]