Best Known (74, 74+17, s)-Nets in Base 25
(74, 74+17, 1048603)-Net over F25 — Constructive and digital
Digital (74, 91, 1048603)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- digital (64, 81, 1048575)-net over F25, using
- net defined by OOA [i] based on linear OOA(2581, 1048575, F25, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2581, 8388601, F25, 17) (dual of [8388601, 8388520, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2581, large, F25, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2581, large, F25, 17) (dual of [large, large−81, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2581, 8388601, F25, 17) (dual of [8388601, 8388520, 18]-code), using
- net defined by OOA [i] based on linear OOA(2581, 1048575, F25, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- digital (2, 10, 28)-net over F25, using
(74, 74+17, large)-Net over F25 — Digital
Digital (74, 91, large)-net over F25, using
- t-expansion [i] based on digital (73, 91, large)-net over F25, using
- 1 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
- 1 times m-reduction [i] based on digital (73, 92, large)-net over F25, using
(74, 74+17, large)-Net in Base 25 — Upper bound on s
There is no (74, 91, large)-net in base 25, because
- 15 times m-reduction [i] would yield (74, 76, large)-net in base 25, but