Best Known (18−10, 18, s)-Nets in Base 25
(18−10, 18, 78)-Net over F25 — Constructive and digital
Digital (8, 18, 78)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (3, 13, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (0, 5, 26)-net over F25, using
(18−10, 18, 144)-Net over F25 — Digital
Digital (8, 18, 144)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2518, 144, F25, 10) (dual of [144, 126, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2518, 208, F25, 10) (dual of [208, 190, 11]-code), using
(18−10, 18, 11698)-Net in Base 25 — Upper bound on s
There is no (8, 18, 11699)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 14 555545 918347 873940 356841 > 2518 [i]