Best Known (34−16, 34, s)-Nets in Base 25
(34−16, 34, 152)-Net over F25 — Constructive and digital
Digital (18, 34, 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, 26, 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
(34−16, 34, 491)-Net over F25 — Digital
Digital (18, 34, 491)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2534, 491, F25, 16) (dual of [491, 457, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2534, 636, F25, 16) (dual of [636, 602, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(2531, 625, F25, 16) (dual of [625, 594, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2523, 625, F25, 12) (dual of [625, 602, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(2534, 636, F25, 16) (dual of [636, 602, 17]-code), using
(34−16, 34, 136997)-Net in Base 25 — Upper bound on s
There is no (18, 34, 136998)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 338828 895660 878617 326856 627909 129209 058555 983745 > 2534 [i]