Best Known (110−28, 110, s)-Nets in Base 25
(110−28, 110, 27903)-Net over F25 — Constructive and digital
Digital (82, 110, 27903)-net over F25, using
- 251 times duplication [i] based on digital (81, 109, 27903)-net over F25, using
- net defined by OOA [i] based on linear OOA(25109, 27903, F25, 28, 28) (dual of [(27903, 28), 781175, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25109, 390642, F25, 28) (dual of [390642, 390533, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25109, 390645, F25, 28) (dual of [390645, 390536, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [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(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(254, 20, F25, 4) (dual of [20, 16, 5]-code or 20-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(25109, 390645, F25, 28) (dual of [390645, 390536, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(25109, 390642, F25, 28) (dual of [390642, 390533, 29]-code), using
- net defined by OOA [i] based on linear OOA(25109, 27903, F25, 28, 28) (dual of [(27903, 28), 781175, 29]-NRT-code), using
(110−28, 110, 318903)-Net over F25 — Digital
Digital (82, 110, 318903)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25110, 318903, F25, 28) (dual of [318903, 318793, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25110, 390650, F25, 28) (dual of [390650, 390540, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [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(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(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(25110, 390650, F25, 28) (dual of [390650, 390540, 29]-code), using
(110−28, 110, large)-Net in Base 25 — Upper bound on s
There is no (82, 110, large)-net in base 25, because
- 26 times m-reduction [i] would yield (82, 84, large)-net in base 25, but