Best Known (32, 32+11, s)-Nets in Base 256
(32, 32+11, 1808281)-Net over F256 — Constructive and digital
Digital (32, 43, 1808281)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 130561)-net over F256, using
- net defined by OOA [i] based on linear OOA(25612, 130561, F256, 5, 5) (dual of [(130561, 5), 652793, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(25612, 261123, F256, 5) (dual of [261123, 261111, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(25612, 261124, F256, 5) (dual of [261124, 261112, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(2561, 65281, F256, 1) (dual of [65281, 65280, 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
- linear OA(2561, 65281, F256, 1) (dual of [65281, 65280, 2]-code) (see above)
- linear OA(2563, 65281, F256, 2) (dual of [65281, 65278, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(2563, 65793, F256, 2) (dual of [65793, 65790, 3]-code), using
- Hamming code H(3,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 65793, F256, 2) (dual of [65793, 65790, 3]-code), using
- linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- linear OA(2561, 65281, F256, 1) (dual of [65281, 65280, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(25612, 261124, F256, 5) (dual of [261124, 261112, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(25612, 261123, F256, 5) (dual of [261123, 261111, 6]-code), using
- net defined by OOA [i] based on linear OOA(25612, 130561, F256, 5, 5) (dual of [(130561, 5), 652793, 6]-NRT-code), using
- digital (20, 31, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- digital (7, 12, 130561)-net over F256, using
(32, 32+11, large)-Net over F256 — Digital
Digital (32, 43, large)-net over F256, using
- t-expansion [i] based on digital (30, 43, large)-net over F256, using
- 1 times m-reduction [i] based on digital (30, 44, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25644, large, F256, 14) (dual of [large, large−44, 15]-code), using
- 4 times code embedding in larger space [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 4 times code embedding in larger space [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25644, large, F256, 14) (dual of [large, large−44, 15]-code), using
- 1 times m-reduction [i] based on digital (30, 44, large)-net over F256, using
(32, 32+11, large)-Net in Base 256 — Upper bound on s
There is no (32, 43, large)-net in base 256, because
- 9 times m-reduction [i] would yield (32, 34, large)-net in base 256, but