Best Known (8, 8+8, s)-Nets in Base 256
(8, 8+8, 16385)-Net over F256 — Constructive and digital
Digital (8, 16, 16385)-net over F256, using
- net defined by OOA [i] based on linear OOA(25616, 16385, F256, 8, 8) (dual of [(16385, 8), 131064, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(25616, 65540, F256, 8) (dual of [65540, 65524, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(25616, 65540, F256, 8) (dual of [65540, 65524, 9]-code), using
(8, 8+8, 32770)-Net over F256 — Digital
Digital (8, 16, 32770)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25616, 32770, F256, 2, 8) (dual of [(32770, 2), 65524, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25616, 65540, F256, 8) (dual of [65540, 65524, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(7) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- OOA 2-folding [i] based on linear OA(25616, 65540, F256, 8) (dual of [65540, 65524, 9]-code), using
(8, 8+8, large)-Net in Base 256 — Upper bound on s
There is no (8, 16, large)-net in base 256, because
- 6 times m-reduction [i] would yield (8, 10, large)-net in base 256, but