Best Known (3, 3+62, s)-Nets in Base 25
(3, 3+62, 52)-Net over F25 — Constructive and digital
Digital (3, 65, 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+62, 56)-Net over F25 — Digital
Digital (3, 65, 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+62, 232)-Net in Base 25 — Upper bound on s
There is no (3, 65, 233)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2565, 233, S25, 62), but
- the linear programming bound shows that M ≥ 44168 144984 128072 314840 190232 509595 889438 688753 607833 925670 067970 538118 680423 611550 622808 863408 863544 464111 328125 / 5928 690910 158229 661957 > 2565 [i]