Best Known (74, 74+27, s)-Nets in Base 25
(74, 74+27, 30048)-Net over F25 — Constructive and digital
Digital (74, 101, 30048)-net over F25, using
- net defined by OOA [i] based on linear OOA(25101, 30048, F25, 27, 27) (dual of [(30048, 27), 811195, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [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]
- OOA 13-folding and stacking with additional row [i] based on linear OA(25101, 390625, F25, 27) (dual of [390625, 390524, 28]-code), using
(74, 74+27, 195314)-Net over F25 — Digital
Digital (74, 101, 195314)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25101, 195314, F25, 2, 27) (dual of [(195314, 2), 390527, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25101, 390628, F25, 27) (dual of [390628, 390527, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25101, 390629, F25, 27) (dual of [390629, 390528, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [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(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(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(25101, 390629, F25, 27) (dual of [390629, 390528, 28]-code), using
- OOA 2-folding [i] based on linear OA(25101, 390628, F25, 27) (dual of [390628, 390527, 28]-code), using
(74, 74+27, large)-Net in Base 25 — Upper bound on s
There is no (74, 101, large)-net in base 25, because
- 25 times m-reduction [i] would yield (74, 76, large)-net in base 25, but