Best Known (66−17, 66, s)-Nets in Base 25
(66−17, 66, 48829)-Net over F25 — Constructive and digital
Digital (49, 66, 48829)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 48829, F25, 17, 17) (dual of [(48829, 17), 830027, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2566, 390633, F25, 17) (dual of [390633, 390567, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, 390635, F25, 17) (dual of [390635, 390569, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(2565, 390626, F25, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2557, 390626, F25, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,8]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2566, 390635, F25, 17) (dual of [390635, 390569, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2566, 390633, F25, 17) (dual of [390633, 390567, 18]-code), using
(66−17, 66, 305693)-Net over F25 — Digital
Digital (49, 66, 305693)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2566, 305693, F25, 17) (dual of [305693, 305627, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, 390635, F25, 17) (dual of [390635, 390569, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(2565, 390626, F25, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2557, 390626, F25, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,8]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2566, 390635, F25, 17) (dual of [390635, 390569, 18]-code), using
(66−17, 66, large)-Net in Base 25 — Upper bound on s
There is no (49, 66, large)-net in base 25, because
- 15 times m-reduction [i] would yield (49, 51, large)-net in base 25, but