Best Known (110−29, 110, s)-Nets in Base 25
(110−29, 110, 27902)-Net over F25 — Constructive and digital
Digital (81, 110, 27902)-net over F25, using
- 251 times duplication [i] based on digital (80, 109, 27902)-net over F25, using
- net defined by OOA [i] based on linear OOA(25109, 27902, F25, 29, 29) (dual of [(27902, 29), 809049, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25109, 390629, F25, 29) (dual of [390629, 390520, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(25109, 390625, F25, 29) (dual of [390625, 390516, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(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(28) ⊂ Ce(27) [i] based on
- OOA 14-folding and stacking with additional row [i] based on linear OA(25109, 390629, F25, 29) (dual of [390629, 390520, 30]-code), using
- net defined by OOA [i] based on linear OOA(25109, 27902, F25, 29, 29) (dual of [(27902, 29), 809049, 30]-NRT-code), using
(110−29, 110, 200310)-Net over F25 — Digital
Digital (81, 110, 200310)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25110, 200310, F25, 29) (dual of [200310, 200200, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25110, 390634, F25, 29) (dual of [390634, 390524, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(25109, 390625, F25, 29) (dual of [390625, 390516, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(25110, 390634, F25, 29) (dual of [390634, 390524, 30]-code), using
(110−29, 110, large)-Net in Base 25 — Upper bound on s
There is no (81, 110, large)-net in base 25, because
- 27 times m-reduction [i] would yield (81, 83, large)-net in base 25, but