Best Known (6, 6+6, s)-Nets in Base 256
(6, 6+6, 21847)-Net over F256 — Constructive and digital
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
(6, 6+6, 36405)-Net over F256 — Digital
Digital (6, 12, 36405)-net over F256, using
- net defined by OOA [i] based on linear OOA(25612, 36405, F256, 6, 6) (dual of [(36405, 6), 218418, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(25612, 36405, F256, 5, 6) (dual of [(36405, 5), 182013, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25612, 36405, F256, 6) (dual of [36405, 36393, 7]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(25612, 65541, F256, 6) (dual of [65541, 65529, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25612, 36405, F256, 6) (dual of [36405, 36393, 7]-code), using
- appending kth column [i] based on linear OOA(25612, 36405, F256, 5, 6) (dual of [(36405, 5), 182013, 7]-NRT-code), using
(6, 6+6, large)-Net in Base 256 — Upper bound on s
There is no (6, 12, large)-net in base 256, because
- 4 times m-reduction [i] would yield (6, 8, large)-net in base 256, but