Best Known (46, 46+14, s)-Nets in Base 25
(46, 46+14, 55830)-Net over F25 — Constructive and digital
Digital (46, 60, 55830)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (39, 53, 55804)-net over F25, using
- net defined by OOA [i] based on linear OOA(2553, 55804, F25, 14, 14) (dual of [(55804, 14), 781203, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2553, 390628, F25, 14) (dual of [390628, 390575, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2553, 390629, F25, 14) (dual of [390629, 390576, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2549, 390625, F25, 13) (dual of [390625, 390576, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2553, 390629, F25, 14) (dual of [390629, 390576, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2553, 390628, F25, 14) (dual of [390628, 390575, 15]-code), using
- net defined by OOA [i] based on linear OOA(2553, 55804, F25, 14, 14) (dual of [(55804, 14), 781203, 15]-NRT-code), using
- digital (0, 7, 26)-net over F25, using
(46, 46+14, 668698)-Net over F25 — Digital
Digital (46, 60, 668698)-net over F25, using
(46, 46+14, large)-Net in Base 25 — Upper bound on s
There is no (46, 60, large)-net in base 25, because
- 12 times m-reduction [i] would yield (46, 48, large)-net in base 25, but