Best Known (77, 77+28, s)-Nets in Base 25
(77, 77+28, 27902)-Net over F25 — Constructive and digital
Digital (77, 105, 27902)-net over F25, using
- net defined by OOA [i] based on linear OOA(25105, 27902, F25, 28, 28) (dual of [(27902, 28), 781151, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25105, 390628, F25, 28) (dual of [390628, 390523, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25105, 390629, F25, 28) (dual of [390629, 390524, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(25105, 390625, F25, 28) (dual of [390625, 390520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(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(27) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(25105, 390629, F25, 28) (dual of [390629, 390524, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(25105, 390628, F25, 28) (dual of [390628, 390523, 29]-code), using
(77, 77+28, 195314)-Net over F25 — Digital
Digital (77, 105, 195314)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25105, 195314, F25, 2, 28) (dual of [(195314, 2), 390523, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25105, 390628, F25, 28) (dual of [390628, 390523, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25105, 390629, F25, 28) (dual of [390629, 390524, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(25105, 390625, F25, 28) (dual of [390625, 390520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(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(27) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(25105, 390629, F25, 28) (dual of [390629, 390524, 29]-code), using
- OOA 2-folding [i] based on linear OA(25105, 390628, F25, 28) (dual of [390628, 390523, 29]-code), using
(77, 77+28, large)-Net in Base 25 — Upper bound on s
There is no (77, 105, large)-net in base 25, because
- 26 times m-reduction [i] would yield (77, 79, large)-net in base 25, but