Best Known (83, 96, s)-Nets in Base 25
(83, 96, 2797176)-Net over F25 — Constructive and digital
Digital (83, 96, 2797176)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 9, 976)-net over F25, using
- net defined by OOA [i] based on linear OOA(259, 976, F25, 4, 4) (dual of [(976, 4), 3895, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(259, 1952, F25, 4) (dual of [1952, 1943, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(259, 1953, F25, 4) (dual of [1953, 1944, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(259, 1952, F25, 4) (dual of [1952, 1943, 5]-code), using
- net defined by OOA [i] based on linear OOA(259, 976, F25, 4, 4) (dual of [(976, 4), 3895, 5]-NRT-code), using
- digital (20, 26, 1398100)-net over F25, using
- s-reduction based on digital (20, 26, 2796201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2526, 2796201, F25, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- s-reduction based on digital (20, 26, 2796201)-net over F25, using
- digital (48, 61, 1398100)-net over F25, using
- net defined by OOA [i] based on linear OOA(2561, 1398100, F25, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2561, 8388601, F25, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2561, 8388601, F25, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(2561, 1398100, F25, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- digital (5, 9, 976)-net over F25, using
(83, 96, large)-Net over F25 — Digital
Digital (83, 96, large)-net over F25, using
- t-expansion [i] based on digital (81, 96, large)-net over F25, using
- 6 times m-reduction [i] based on digital (81, 102, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25102, large, F25, 21) (dual of [large, large−102, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25102, large, F25, 21) (dual of [large, large−102, 22]-code), using
- 6 times m-reduction [i] based on digital (81, 102, large)-net over F25, using
(83, 96, large)-Net in Base 25 — Upper bound on s
There is no (83, 96, large)-net in base 25, because
- 11 times m-reduction [i] would yield (83, 85, large)-net in base 25, but