Best Known (39, 39+13, s)-Nets in Base 25
(39, 39+13, 65107)-Net over F25 — Constructive and digital
Digital (39, 52, 65107)-net over F25, using
- net defined by OOA [i] based on linear OOA(2552, 65107, F25, 13, 13) (dual of [(65107, 13), 846339, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2552, 390643, F25, 13) (dual of [390643, 390591, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 390645, F25, 13) (dual of [390645, 390593, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(2549, 390626, F25, 13) (dual of [390626, 390577, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2533, 390626, F25, 9) (dual of [390626, 390593, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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([0,6]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2552, 390645, F25, 13) (dual of [390645, 390593, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2552, 390643, F25, 13) (dual of [390643, 390591, 14]-code), using
(39, 39+13, 390645)-Net over F25 — Digital
Digital (39, 52, 390645)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2552, 390645, F25, 13) (dual of [390645, 390593, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(2549, 390626, F25, 13) (dual of [390626, 390577, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2533, 390626, F25, 9) (dual of [390626, 390593, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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([0,6]) ⊂ C([0,4]) [i] based on
(39, 39+13, large)-Net in Base 25 — Upper bound on s
There is no (39, 52, large)-net in base 25, because
- 11 times m-reduction [i] would yield (39, 41, large)-net in base 25, but