Best Known (49−11, 49, s)-Nets in Base 25
(49−11, 49, 78426)-Net over F25 — Constructive and digital
Digital (38, 49, 78426)-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 (31, 42, 78126)-net over F25, using
- net defined by OOA [i] based on linear OOA(2542, 78126, F25, 11, 11) (dual of [(78126, 11), 859344, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2542, 390631, F25, 11) (dual of [390631, 390589, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2542, 390635, F25, 11) (dual of [390635, 390593, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(2541, 390626, F25, 11) (dual of [390626, 390585, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2533, 390626, F25, 9) (dual of [390626, 390593, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2542, 390635, F25, 11) (dual of [390635, 390593, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2542, 390631, F25, 11) (dual of [390631, 390589, 12]-code), using
- net defined by OOA [i] based on linear OOA(2542, 78126, F25, 11, 11) (dual of [(78126, 11), 859344, 12]-NRT-code), using
- digital (2, 7, 300)-net over F25, using
(49−11, 49, 1335589)-Net over F25 — Digital
Digital (38, 49, 1335589)-net over F25, using
(49−11, 49, large)-Net in Base 25 — Upper bound on s
There is no (38, 49, large)-net in base 25, because
- 9 times m-reduction [i] would yield (38, 40, large)-net in base 25, but