Best Known (83, 83+19, s)-Nets in Base 25
(83, 83+19, 932094)-Net over F25 — Constructive and digital
Digital (83, 102, 932094)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
- digital (72, 91, 932066)-net over F25, using
- net defined by OOA [i] based on linear OOA(2591, 932066, F25, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2591, 8388595, F25, 19) (dual of [8388595, 8388504, 20]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2591, large, F25, 19) (dual of [large, large−91, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2591, 8388595, F25, 19) (dual of [8388595, 8388504, 20]-code), using
- net defined by OOA [i] based on linear OOA(2591, 932066, F25, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- digital (2, 11, 28)-net over F25, using
(83, 83+19, large)-Net over F25 — Digital
Digital (83, 102, large)-net over F25, using
- t-expansion [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
(83, 83+19, large)-Net in Base 25 — Upper bound on s
There is no (83, 102, large)-net in base 25, because
- 17 times m-reduction [i] would yield (83, 85, large)-net in base 25, but