Best Known (26, 54, s)-Nets in Base 25
(26, 54, 200)-Net over F25 — Constructive and digital
Digital (26, 54, 200)-net over F25, using
- t-expansion [i] based on digital (25, 54, 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
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(26, 54, 315)-Net over F25 — Digital
Digital (26, 54, 315)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2554, 315, F25, 2, 28) (dual of [(315, 2), 576, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2554, 630, F25, 28) (dual of [630, 576, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2554, 631, F25, 28) (dual of [631, 577, 29]-code), using
- construction XX applied to C1 = C([0,26]), C2 = C([3,27]), C3 = C1 + C2 = C([3,26]), and C∩ = C1 ∩ C2 = C([0,27]) [i] based on
- linear OA(2550, 624, F25, 27) (dual of [624, 574, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2549, 624, F25, 25) (dual of [624, 575, 26]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,27}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2552, 624, F25, 28) (dual of [624, 572, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2547, 624, F25, 24) (dual of [624, 577, 25]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,26}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to C1 = C([0,26]), C2 = C([3,27]), C3 = C1 + C2 = C([3,26]), and C∩ = C1 ∩ C2 = C([0,27]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2554, 631, F25, 28) (dual of [631, 577, 29]-code), using
- OOA 2-folding [i] based on linear OA(2554, 630, F25, 28) (dual of [630, 576, 29]-code), using
(26, 54, 62122)-Net in Base 25 — Upper bound on s
There is no (26, 54, 62123)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 3081 598957 782232 704214 216062 410164 235387 399307 707309 492851 351856 057848 245745 > 2554 [i]