Best Known (63−32, 63, s)-Nets in Base 25
(63−32, 63, 204)-Net over F25 — Constructive and digital
Digital (31, 63, 204)-net over F25, using
- t-expansion [i] based on digital (30, 63, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
(63−32, 63, 376)-Net over F25 — Digital
Digital (31, 63, 376)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2563, 376, F25, 32) (dual of [376, 313, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2563, 624, F25, 32) (dual of [624, 561, 33]-code), using
(63−32, 63, 90505)-Net in Base 25 — Upper bound on s
There is no (31, 63, 90506)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 11755 068874 385036 845722 193489 052535 557084 913174 339214 090747 277128 273924 793853 822247 866625 > 2563 [i]