Best Known (24, 32, s)-Nets in Base 25
(24, 32, 97661)-Net over F25 — Constructive and digital
Digital (24, 32, 97661)-net over F25, using
- net defined by OOA [i] based on linear OOA(2532, 97661, F25, 8, 8) (dual of [(97661, 8), 781256, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2532, 390644, F25, 8) (dual of [390644, 390612, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- linear OA(2529, 390625, F25, 8) (dual of [390625, 390596, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-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 Ce(7) ⊂ Ce(3) [i] based on
- OA 4-folding and stacking [i] based on linear OA(2532, 390644, F25, 8) (dual of [390644, 390612, 9]-code), using
(24, 32, 390644)-Net over F25 — Digital
Digital (24, 32, 390644)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2532, 390644, F25, 8) (dual of [390644, 390612, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- linear OA(2529, 390625, F25, 8) (dual of [390625, 390596, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-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 Ce(7) ⊂ Ce(3) [i] based on
(24, 32, large)-Net in Base 25 — Upper bound on s
There is no (24, 32, large)-net in base 25, because
- 6 times m-reduction [i] would yield (24, 26, large)-net in base 25, but