Best Known (23−5, 23, s)-Nets in Base 25
(23−5, 23, 4194327)-Net over F25 — Constructive and digital
Digital (18, 23, 4194327)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 26)-net over F25, using
- digital (16, 21, 4194301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2521, 4194301, F25, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2521, 4194301, F25, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
(23−5, 23, large)-Net over F25 — Digital
Digital (18, 23, large)-net over F25, using
- 252 times duplication [i] based on digital (16, 21, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
(23−5, 23, large)-Net in Base 25 — Upper bound on s
There is no (18, 23, large)-net in base 25, because
- 3 times m-reduction [i] would yield (18, 20, large)-net in base 25, but