Best Known (37−4, 37, s)-Nets in Base 25
(37−4, 37, large)-Net over F25 — Constructive and digital
Digital (33, 37, large)-net over F25, using
- 258 times duplication [i] based on digital (25, 29, large)-net over F25, using
- t-expansion [i] based on digital (24, 29, large)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 6, large)-net over F25, using
- 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
- (u, u+v)-construction [i] based on
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (24, 29, large)-net over F25, using
(37−4, 37, large)-Net in Base 25 — Upper bound on s
There is no (33, 37, large)-net in base 25, because
- 2 times m-reduction [i] would yield (33, 35, large)-net in base 25, but