Best Known (56−26, 56, s)-Nets in Base 25
(56−26, 56, 204)-Net over F25 — Constructive and digital
Digital (30, 56, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
(56−26, 56, 642)-Net over F25 — Digital
Digital (30, 56, 642)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2556, 642, F25, 26) (dual of [642, 586, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, 646, F25, 26) (dual of [646, 590, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2535, 625, F25, 18) (dual of [625, 590, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(257, 21, F25, 7) (dual of [21, 14, 8]-code or 21-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(25) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2556, 646, F25, 26) (dual of [646, 590, 27]-code), using
(56−26, 56, 248358)-Net in Base 25 — Upper bound on s
There is no (30, 56, 248359)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1 925986 613982 674108 345735 723461 742055 964164 030466 134126 185175 363276 767971 920265 > 2556 [i]