Best Known (57−42, 57, s)-Nets in Base 25
(57−42, 57, 126)-Net over F25 — Constructive and digital
Digital (15, 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
(57−42, 57, 140)-Net over F25 — Digital
Digital (15, 57, 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
(57−42, 57, 2241)-Net in Base 25 — Upper bound on s
There is no (15, 57, 2242)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 48 252731 360476 794483 266534 588379 973973 133254 339738 046690 126565 350126 163732 543345 > 2557 [i]