Best Known (44−4, 44, s)-Nets in Base 5
(44−4, 44, large)-Net over F5 — Constructive and digital
Digital (40, 44, large)-net over F5, using
- t-expansion [i] based on digital (39, 44, large)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 6)-net over F5, using
- digital (37, 42, 8388602)-net over F5, using
- trace code for nets [i] based on 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
- trace code for nets [i] based on digital (16, 21, 4194301)-net over F25, using
- (u, u+v)-construction [i] based on
(44−4, 44, large)-Net in Base 5 — Upper bound on s
There is no (40, 44, large)-net in base 5, because
- 2 times m-reduction [i] would yield (40, 42, large)-net in base 5, but