Best Known (99−25, 99, s)-Nets in Base 25
(99−25, 99, 32553)-Net over F25 — Constructive and digital
Digital (74, 99, 32553)-net over F25, using
- net defined by OOA [i] based on linear OOA(2599, 32553, F25, 25, 25) (dual of [(32553, 25), 813726, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2599, 390637, F25, 25) (dual of [390637, 390538, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using
- 1 times truncation [i] based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- 1 times truncation [i] based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2599, 390637, F25, 25) (dual of [390637, 390538, 26]-code), using
(99−25, 99, 355362)-Net over F25 — Digital
Digital (74, 99, 355362)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2599, 355362, F25, 25) (dual of [355362, 355263, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using
- 1 times truncation [i] based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(2597, 390625, F25, 26) (dual of [390625, 390528, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- 1 times truncation [i] based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using
(99−25, 99, large)-Net in Base 25 — Upper bound on s
There is no (74, 99, large)-net in base 25, because
- 23 times m-reduction [i] would yield (74, 76, large)-net in base 25, but