Best Known (30−9, 30, s)-Nets in Base 25
(30−9, 30, 3934)-Net over F25 — Constructive and digital
Digital (21, 30, 3934)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (17, 26, 3908)-net over F25, using
- net defined by OOA [i] based on linear OOA(2526, 3908, F25, 9, 9) (dual of [(3908, 9), 35146, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2526, 15633, F25, 9) (dual of [15633, 15607, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(2519, 15626, F25, 7) (dual of [15626, 15607, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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([0,4]) ⊂ C([0,3]) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2526, 15633, F25, 9) (dual of [15633, 15607, 10]-code), using
- net defined by OOA [i] based on linear OOA(2526, 3908, F25, 9, 9) (dual of [(3908, 9), 35146, 10]-NRT-code), using
- digital (0, 4, 26)-net over F25, using
(30−9, 30, 27404)-Net over F25 — Digital
Digital (21, 30, 27404)-net over F25, using
(30−9, 30, large)-Net in Base 25 — Upper bound on s
There is no (21, 30, large)-net in base 25, because
- 7 times m-reduction [i] would yield (21, 23, large)-net in base 25, but