Best Known (75, 100, s)-Nets in Base 25
(75, 100, 32553)-Net over F25 — Constructive and digital
Digital (75, 100, 32553)-net over F25, using
- 251 times duplication [i] based on digital (74, 99, 32553)-net over F25, using
- net defined by OOA [i] based on linear OOA(2599, 32553, F25, 25, 25) (dual of [(32553, 25), 813726, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2599, 390637, F25, 25) (dual of [390637, 390538, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using
- 1 times truncation [i] 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
- 1 times truncation [i] based on linear OA(25100, 390640, F25, 26) (dual of [390640, 390540, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2599, 390639, F25, 25) (dual of [390639, 390540, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2599, 390637, F25, 25) (dual of [390637, 390538, 26]-code), using
- net defined by OOA [i] based on linear OOA(2599, 32553, F25, 25, 25) (dual of [(32553, 25), 813726, 26]-NRT-code), using
(75, 100, 390645)-Net over F25 — Digital
Digital (75, 100, 390645)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25100, 390645, F25, 25) (dual of [390645, 390545, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2597, 390626, F25, 25) (dual of [390626, 390529, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2581, 390626, F25, 21) (dual of [390626, 390545, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-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 C([0,12]) ⊂ C([0,10]) [i] based on
(75, 100, large)-Net in Base 25 — Upper bound on s
There is no (75, 100, large)-net in base 25, because
- 23 times m-reduction [i] would yield (75, 77, large)-net in base 25, but