Best Known (45−42, 45, s)-Nets in Base 25
(45−42, 45, 52)-Net over F25 — Constructive and digital
Digital (3, 45, 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
(45−42, 45, 56)-Net over F25 — Digital
Digital (3, 45, 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
(45−42, 45, 278)-Net in Base 25 — Upper bound on s
There is no (3, 45, 279)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2545, 279, S25, 42), but
- the linear programming bound shows that M ≥ 894865 265323 213813 515907 032287 172689 552041 533983 355037 218387 906250 427477 061748 504638 671875 / 1094 375929 231920 030060 222283 > 2545 [i]