Best Known (18, 18+17, s)-Nets in Base 25
(18, 18+17, 152)-Net over F25 — Constructive and digital
Digital (18, 35, 152)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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 (10, 27, 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
- digital (0, 8, 26)-net over F25, using
(18, 18+17, 388)-Net over F25 — Digital
Digital (18, 35, 388)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2535, 388, F25, 17) (dual of [388, 353, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2535, 633, F25, 17) (dual of [633, 598, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(2533, 625, F25, 17) (dual of [625, 592, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2527, 625, F25, 14) (dual of [625, 598, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2535, 633, F25, 17) (dual of [633, 598, 18]-code), using
(18, 18+17, 136997)-Net in Base 25 — Upper bound on s
There is no (18, 35, 136998)-net in base 25, because
- 1 times m-reduction [i] would yield (18, 34, 136998)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 338828 895660 878617 326856 627909 129209 058555 983745 > 2534 [i]