Best Known (85−12, 85, s)-Nets in Base 25
(85−12, 85, 2796200)-Net over F25 — Constructive and digital
Digital (73, 85, 2796200)-net over F25, using
- 253 times duplication [i] based on 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), 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]
- discarding factors / shortening the dual code based on linear OA(2526, large, F25, 6) (dual of [large, large−26, 7]-code), using
- 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
(85−12, 85, large)-Net over F25 — Digital
Digital (73, 85, large)-net over F25, using
- 7 times m-reduction [i] based on digital (73, 92, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2592, large, F25, 19) (dual of [large, large−92, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2591, large, F25, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(2591, large, F25, 19) (dual of [large, large−91, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2592, large, F25, 19) (dual of [large, large−92, 20]-code), using
(85−12, 85, large)-Net in Base 25 — Upper bound on s
There is no (73, 85, large)-net in base 25, because
- 10 times m-reduction [i] would yield (73, 75, large)-net in base 25, but