Best Known (67−32, 67, s)-Nets in Base 25
(67−32, 67, 230)-Net over F25 — Constructive and digital
Digital (35, 67, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 25, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (10, 42, 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 (9, 25, 104)-net over F25, using
(67−32, 67, 583)-Net over F25 — Digital
Digital (35, 67, 583)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2567, 583, F25, 32) (dual of [583, 516, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2567, 645, F25, 32) (dual of [645, 578, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(23) [i] based on
- linear OA(2560, 625, F25, 32) (dual of [625, 565, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2547, 625, F25, 24) (dual of [625, 578, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(257, 20, F25, 7) (dual of [20, 13, 8]-code or 20-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- construction X applied to Ce(31) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(2567, 645, F25, 32) (dual of [645, 578, 33]-code), using
(67−32, 67, 202387)-Net in Base 25 — Upper bound on s
There is no (35, 67, 202388)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4591 946250 923444 417538 870008 390412 020793 416618 547069 213398 519773 041965 633124 776420 379376 065025 > 2567 [i]