Best Known (53−38, 53, s)-Nets in Base 25
(53−38, 53, 126)-Net over F25 — Constructive and digital
Digital (15, 53, 126)-net over F25, using
- t-expansion [i] based on digital (10, 53, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(53−38, 53, 140)-Net over F25 — Digital
Digital (15, 53, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(53−38, 53, 2611)-Net in Base 25 — Upper bound on s
There is no (15, 53, 2612)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 123 668038 261788 638292 981859 444218 051154 457140 629530 189286 832329 954185 416225 > 2553 [i]