Best Known (41, 41+5, s)-Nets in Base 5
(41, 41+5, large)-Net over F5 — Constructive and digital
Digital (41, 46, large)-net over F5, using
- trace code for nets [i] based on digital (18, 23, 4194326)-net over F25, using
- net defined by OOA [i] based on linear OOA(2523, 4194326, F25, 6, 5) (dual of [(4194326, 6), 25165933, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2523, 4194327, F25, 2, 5) (dual of [(4194327, 2), 8388631, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(252, 26, F25, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;50,25) [i]
- linear OOA(2521, 4194301, F25, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2521, 8388602, F25, 5) (dual of [8388602, 8388581, 6]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- OOA 2-folding [i] based on linear OA(2521, 8388602, F25, 5) (dual of [8388602, 8388581, 6]-code), using
- linear OOA(252, 26, F25, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(2523, 4194327, F25, 2, 5) (dual of [(4194327, 2), 8388631, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2523, 4194326, F25, 6, 5) (dual of [(4194326, 6), 25165933, 6]-NRT-code), using
(41, 41+5, large)-Net in Base 5 — Upper bound on s
There is no (41, 46, large)-net in base 5, because
- 3 times m-reduction [i] would yield (41, 43, large)-net in base 5, but