Best Known (46−12, 46, s)-Nets in Base 256
(46−12, 46, 1419947)-Net over F256 — Constructive and digital
Digital (34, 46, 1419947)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (6, 12, 21847)-net over F256, using
- net defined by OOA [i] based on linear OOA(25612, 21847, F256, 6, 6) (dual of [(21847, 6), 131070, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25612, 65541, F256, 6) (dual of [65541, 65529, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2567, 65536, F256, 4) (dual of [65536, 65529, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(25612, 65541, F256, 6) (dual of [65541, 65529, 7]-code), using
- net defined by OOA [i] based on linear OOA(25612, 21847, F256, 6, 6) (dual of [(21847, 6), 131070, 7]-NRT-code), using
- digital (22, 34, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25634, 1398100, F256, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- net defined by OOA [i] based on linear OOA(25634, 1398100, F256, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
- digital (6, 12, 21847)-net over F256, using
(46−12, 46, large)-Net over F256 — Digital
Digital (34, 46, large)-net over F256, using
- t-expansion [i] based on digital (33, 46, large)-net over F256, using
- 2 times m-reduction [i] based on digital (33, 48, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25648, large, F256, 15) (dual of [large, large−48, 16]-code), using
- 5 times code embedding in larger space [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 5 times code embedding in larger space [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25648, large, F256, 15) (dual of [large, large−48, 16]-code), using
- 2 times m-reduction [i] based on digital (33, 48, large)-net over F256, using
(46−12, 46, large)-Net in Base 256 — Upper bound on s
There is no (34, 46, large)-net in base 256, because
- 10 times m-reduction [i] would yield (34, 36, large)-net in base 256, but