Best Known (96, 96+12, s)-Nets in Base 25
(96, 96+12, 5592400)-Net over F25 — Constructive and digital
Digital (96, 108, 5592400)-net over F25, using
- (u, u+v)-construction [i] 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
- digital (70, 82, 2796200)-net over F25, using
- net defined by OOA [i] based on linear OOA(2582, 2796200, F25, 14, 12) (dual of [(2796200, 14), 39146718, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2582, 8388601, F25, 2, 12) (dual of [(8388601, 2), 16777120, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2582, 8388602, F25, 2, 12) (dual of [(8388602, 2), 16777122, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2526, 4194301, F25, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2526, 8388602, F25, 6) (dual of [8388602, 8388576, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code) (see above)
- OOA 2-folding [i] based on linear OA(2526, 8388602, F25, 6) (dual of [8388602, 8388576, 7]-code), using
- linear OOA(2556, 4194301, F25, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- linear OOA(2526, 4194301, F25, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2582, 8388602, F25, 2, 12) (dual of [(8388602, 2), 16777122, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2582, 8388601, F25, 2, 12) (dual of [(8388601, 2), 16777120, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2582, 2796200, F25, 14, 12) (dual of [(2796200, 14), 39146718, 13]-NRT-code), using
- digital (20, 26, 2796201)-net over F25, using
(96, 96+12, large)-Net over F25 — Digital
Digital (96, 108, large)-net over F25, using
- 251 times duplication [i] based on digital (95, 107, large)-net over F25, using
- t-expansion [i] based on digital (85, 107, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25107, large, F25, 22) (dual of [large, large−107, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25106, large, F25, 22) (dual of [large, large−106, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times code embedding in larger space [i] based on linear OA(25106, large, F25, 22) (dual of [large, large−106, 23]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25107, large, F25, 22) (dual of [large, large−107, 23]-code), using
- t-expansion [i] based on digital (85, 107, large)-net over F25, using
(96, 96+12, large)-Net in Base 25 — Upper bound on s
There is no (96, 108, large)-net in base 25, because
- 10 times m-reduction [i] would yield (96, 98, large)-net in base 25, but