Best Known (106−28, 106, s)-Nets in Base 25
(106−28, 106, 27902)-Net over F25 — Constructive and digital
Digital (78, 106, 27902)-net over F25, using
- 251 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(25105, 27902, F25, 28, 28) (dual of [(27902, 28), 781151, 29]-NRT-code), using
(106−28, 106, 195317)-Net over F25 — Digital
Digital (78, 106, 195317)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25106, 195317, F25, 2, 28) (dual of [(195317, 2), 390528, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25106, 390634, F25, 28) (dual of [390634, 390528, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(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(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(25106, 390634, F25, 28) (dual of [390634, 390528, 29]-code), using
(106−28, 106, large)-Net in Base 25 — Upper bound on s
There is no (78, 106, large)-net in base 25, because
- 26 times m-reduction [i] would yield (78, 80, large)-net in base 25, but