Best Known (47, 70, s)-Nets in Base 25
(47, 70, 1421)-Net over F25 — Constructive and digital
Digital (47, 70, 1421)-net over F25, using
- 252 times duplication [i] based on digital (45, 68, 1421)-net over F25, using
- net defined by OOA [i] based on linear OOA(2568, 1421, F25, 23, 23) (dual of [(1421, 23), 32615, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2568, 15632, F25, 23) (dual of [15632, 15564, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2568, 15633, F25, 23) (dual of [15633, 15565, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(2567, 15626, F25, 23) (dual of [15626, 15559, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (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(251, 7, F25, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2568, 15633, F25, 23) (dual of [15633, 15565, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2568, 15632, F25, 23) (dual of [15632, 15564, 24]-code), using
- net defined by OOA [i] based on linear OOA(2568, 1421, F25, 23, 23) (dual of [(1421, 23), 32615, 24]-NRT-code), using
(47, 70, 14164)-Net over F25 — Digital
Digital (47, 70, 14164)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2570, 14164, F25, 23) (dual of [14164, 14094, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2570, 15641, F25, 23) (dual of [15641, 15571, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(2567, 15626, F25, 23) (dual of [15626, 15559, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2555, 15626, F25, 19) (dual of [15626, 15571, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2570, 15641, F25, 23) (dual of [15641, 15571, 24]-code), using
(47, 70, large)-Net in Base 25 — Upper bound on s
There is no (47, 70, large)-net in base 25, because
- 21 times m-reduction [i] would yield (47, 49, large)-net in base 25, but