Best Known (28, 28+11, s)-Nets in Base 25
(28, 28+11, 3426)-Net over F25 — Constructive and digital
Digital (28, 39, 3426)-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 (21, 32, 3126)-net over F25, using
- net defined by OOA [i] based on linear OOA(2532, 3126, F25, 11, 11) (dual of [(3126, 11), 34354, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2532, 15631, F25, 11) (dual of [15631, 15599, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2532, 15633, F25, 11) (dual of [15633, 15601, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [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]
- linear OA(2525, 15626, F25, 9) (dual of [15626, 15601, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 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(2532, 15633, F25, 11) (dual of [15633, 15601, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2532, 15631, F25, 11) (dual of [15631, 15599, 12]-code), using
- net defined by OOA [i] based on linear OOA(2532, 3126, F25, 11, 11) (dual of [(3126, 11), 34354, 12]-NRT-code), using
- digital (2, 7, 300)-net over F25, using
(28, 28+11, 53428)-Net over F25 — Digital
Digital (28, 39, 53428)-net over F25, using
(28, 28+11, large)-Net in Base 25 — Upper bound on s
There is no (28, 39, large)-net in base 25, because
- 9 times m-reduction [i] would yield (28, 30, large)-net in base 25, but