Best Known (10, 10+10, s)-Nets in Base 25
(10, 10+10, 126)-Net over F25 — Constructive and digital
Digital (10, 20, 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
(10, 10+10, 325)-Net over F25 — Digital
Digital (10, 20, 325)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2520, 325, F25, 10) (dual of [325, 305, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2520, 624, F25, 10) (dual of [624, 604, 11]-code), using
(10, 10+10, 42399)-Net in Base 25 — Upper bound on s
There is no (10, 20, 42400)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 9095 306489 800993 854816 971521 > 2520 [i]