Best Known (25, 34, s)-Nets in Base 25
(25, 34, 97658)-Net over F25 — Constructive and digital
Digital (25, 34, 97658)-net over F25, using
- net defined by OOA [i] based on linear OOA(2534, 97658, F25, 9, 9) (dual of [(97658, 9), 878888, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2534, 390633, F25, 9) (dual of [390633, 390599, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2534, 390635, F25, 9) (dual of [390635, 390601, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(2525, 390626, F25, 7) (dual of [390626, 390601, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [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 C([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2534, 390635, F25, 9) (dual of [390635, 390601, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2534, 390633, F25, 9) (dual of [390633, 390599, 10]-code), using
(25, 34, 390636)-Net over F25 — Digital
Digital (25, 34, 390636)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2534, 390636, F25, 9) (dual of [390636, 390602, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(2525, 390626, F25, 7) (dual of [390626, 390601, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(259, 10, F25, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
- dual of repetition code with length 10 [i]
- linear OA(251, 10, F25, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
(25, 34, large)-Net in Base 25 — Upper bound on s
There is no (25, 34, large)-net in base 25, because
- 7 times m-reduction [i] would yield (25, 27, large)-net in base 25, but