Best Known (104−27, 104, s)-Nets in Base 25
(104−27, 104, 30049)-Net over F25 — Constructive and digital
Digital (77, 104, 30049)-net over F25, using
- net defined by OOA [i] based on linear OOA(25104, 30049, F25, 27, 27) (dual of [(30049, 27), 811219, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25104, 390638, F25, 27) (dual of [390638, 390534, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25104, 390640, F25, 27) (dual of [390640, 390536, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(25101, 390625, F25, 27) (dual of [390625, 390524, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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 Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(25104, 390640, F25, 27) (dual of [390640, 390536, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25104, 390638, F25, 27) (dual of [390638, 390534, 28]-code), using
(104−27, 104, 243728)-Net over F25 — Digital
Digital (77, 104, 243728)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25104, 243728, F25, 27) (dual of [243728, 243624, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25104, 390640, F25, 27) (dual of [390640, 390536, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(25101, 390625, F25, 27) (dual of [390625, 390524, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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 Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(25104, 390640, F25, 27) (dual of [390640, 390536, 28]-code), using
(104−27, 104, large)-Net in Base 25 — Upper bound on s
There is no (77, 104, large)-net in base 25, because
- 25 times m-reduction [i] would yield (77, 79, large)-net in base 25, but