Best Known (28−9, 28, s)-Nets in Base 25
(28−9, 28, 3910)-Net over F25 — Constructive and digital
Digital (19, 28, 3910)-net over F25, using
- net defined by OOA [i] based on linear OOA(2528, 3910, F25, 9, 9) (dual of [(3910, 9), 35162, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2528, 15641, F25, 9) (dual of [15641, 15613, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,2]) [i] based on
- linear OA(2525, 15626, F25, 9) (dual of [15626, 15601, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2513, 15626, F25, 5) (dual of [15626, 15613, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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([0,4]) ⊂ C([0,2]) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2528, 15641, F25, 9) (dual of [15641, 15613, 10]-code), using
(28−9, 28, 15641)-Net over F25 — Digital
Digital (19, 28, 15641)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2528, 15641, F25, 9) (dual of [15641, 15613, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,2]) [i] based on
- linear OA(2525, 15626, F25, 9) (dual of [15626, 15601, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2513, 15626, F25, 5) (dual of [15626, 15613, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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([0,4]) ⊂ C([0,2]) [i] based on
(28−9, 28, large)-Net in Base 25 — Upper bound on s
There is no (19, 28, large)-net in base 25, because
- 7 times m-reduction [i] would yield (19, 21, large)-net in base 25, but