Best Known (25, 25+24, s)-Nets in Base 25
(25, 25+24, 200)-Net over F25 — Constructive and digital
Digital (25, 49, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
(25, 25+24, 413)-Net over F25 — Digital
Digital (25, 49, 413)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2549, 413, F25, 24) (dual of [413, 364, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2549, 633, F25, 24) (dual of [633, 584, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- 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(2541, 625, F25, 21) (dual of [625, 584, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2549, 633, F25, 24) (dual of [633, 584, 25]-code), using
(25, 25+24, 112559)-Net in Base 25 — Upper bound on s
There is no (25, 49, 112560)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 315 562028 294928 753887 543299 212161 586152 305799 376983 061056 288954 479105 > 2549 [i]