Best Known (57−46, 57, s)-Nets in Base 25
(57−46, 57, 126)-Net over F25 — Constructive and digital
Digital (11, 57, 126)-net over F25, using
- t-expansion [i] based on digital (10, 57, 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
(57−46, 57, 1132)-Net in Base 25 — Upper bound on s
There is no (11, 57, 1133)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 48 336596 041135 338082 728694 239772 040214 483989 467668 137971 878738 588878 884679 079625 > 2557 [i]