Best Known (101−26, 101, s)-Nets in Base 25
(101−26, 101, 30049)-Net over F25 — Constructive and digital
Digital (75, 101, 30049)-net over F25, using
- 251 times duplication [i] based on digital (74, 100, 30049)-net over F25, using
- net defined by OOA [i] based on linear OOA(25100, 30049, F25, 26, 26) (dual of [(30049, 26), 781174, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25100, 390637, F25, 26) (dual of [390637, 390537, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 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(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(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25100, 390637, F25, 26) (dual of [390637, 390537, 27]-code), using
- net defined by OOA [i] based on linear OOA(25100, 30049, F25, 26, 26) (dual of [(30049, 26), 781174, 27]-NRT-code), using
(101−26, 101, 272824)-Net over F25 — Digital
Digital (75, 101, 272824)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25101, 272824, F25, 26) (dual of [272824, 272723, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25101, 390645, F25, 26) (dual of [390645, 390544, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- 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(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(25101, 390645, F25, 26) (dual of [390645, 390544, 27]-code), using
(101−26, 101, large)-Net in Base 25 — Upper bound on s
There is no (75, 101, large)-net in base 25, because
- 24 times m-reduction [i] would yield (75, 77, large)-net in base 25, but