Best Known (27, 27+11, s)-Nets in Base 25
(27, 27+11, 3425)-Net over F25 — Constructive and digital
Digital (27, 38, 3425)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- digital (20, 31, 3125)-net over F25, using
- net defined by OOA [i] based on linear OOA(2531, 3125, F25, 11, 11) (dual of [(3125, 11), 34344, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2531, 15626, F25, 11) (dual of [15626, 15595, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(2531, 15626, F25, 11) (dual of [15626, 15595, 12]-code), using
- net defined by OOA [i] based on linear OOA(2531, 3125, F25, 11, 11) (dual of [(3125, 11), 34344, 12]-NRT-code), using
- digital (2, 7, 300)-net over F25, using
(27, 27+11, 38725)-Net over F25 — Digital
Digital (27, 38, 38725)-net over F25, using
(27, 27+11, large)-Net in Base 25 — Upper bound on s
There is no (27, 38, large)-net in base 25, because
- 9 times m-reduction [i] would yield (27, 29, large)-net in base 25, but