Best Known (51, 76, s)-Nets in Base 25
(51, 76, 1303)-Net over F25 — Constructive and digital
Digital (51, 76, 1303)-net over F25, using
- net defined by OOA [i] based on linear OOA(2576, 1303, F25, 25, 25) (dual of [(1303, 25), 32499, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2576, 15637, F25, 25) (dual of [15637, 15561, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, 15641, F25, 25) (dual of [15641, 15565, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2561, 15626, F25, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-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 C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2576, 15641, F25, 25) (dual of [15641, 15565, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2576, 15637, F25, 25) (dual of [15637, 15561, 26]-code), using
(51, 76, 14204)-Net over F25 — Digital
Digital (51, 76, 14204)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2576, 14204, F25, 25) (dual of [14204, 14128, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, 15641, F25, 25) (dual of [15641, 15565, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2561, 15626, F25, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-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 C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2576, 15641, F25, 25) (dual of [15641, 15565, 26]-code), using
(51, 76, large)-Net in Base 25 — Upper bound on s
There is no (51, 76, large)-net in base 25, because
- 23 times m-reduction [i] would yield (51, 53, large)-net in base 25, but