Best Known (40−26, 40, s)-Nets in Base 25
(40−26, 40, 126)-Net over F25 — Constructive and digital
Digital (14, 40, 126)-net over F25, using
- t-expansion [i] based on digital (10, 40, 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
(40−26, 40, 130)-Net over F25 — Digital
Digital (14, 40, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(40−26, 40, 4720)-Net in Base 25 — Upper bound on s
There is no (14, 40, 4721)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 82 932155 073633 254482 850376 174704 598329 701746 945877 358905 > 2540 [i]