Best Known (34, 68, s)-Nets in Base 256
(34, 68, 3855)-Net over F256 — Constructive and digital
Digital (34, 68, 3855)-net over F256, using
- 2561 times duplication [i] based on digital (33, 67, 3855)-net over F256, using
- net defined by OOA [i] based on linear OOA(25667, 3855, F256, 34, 34) (dual of [(3855, 34), 131003, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(25667, 65535, F256, 34) (dual of [65535, 65468, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(25667, 65536, F256, 34) (dual of [65536, 65469, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(25667, 65536, F256, 34) (dual of [65536, 65469, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(25667, 65535, F256, 34) (dual of [65535, 65468, 35]-code), using
- net defined by OOA [i] based on linear OOA(25667, 3855, F256, 34, 34) (dual of [(3855, 34), 131003, 35]-NRT-code), using
(34, 68, 11602)-Net over F256 — Digital
Digital (34, 68, 11602)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25668, 11602, F256, 5, 34) (dual of [(11602, 5), 57942, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25668, 13108, F256, 5, 34) (dual of [(13108, 5), 65472, 35]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25668, 65540, F256, 34) (dual of [65540, 65472, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(25668, 65541, F256, 34) (dual of [65541, 65473, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(31) [i] based on
- linear OA(25667, 65536, F256, 34) (dual of [65536, 65469, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(25663, 65536, F256, 32) (dual of [65536, 65473, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(33) ⊂ Ce(31) [i] based on
- discarding factors / shortening the dual code based on linear OA(25668, 65541, F256, 34) (dual of [65541, 65473, 35]-code), using
- OOA 5-folding [i] based on linear OA(25668, 65540, F256, 34) (dual of [65540, 65472, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(25668, 13108, F256, 5, 34) (dual of [(13108, 5), 65472, 35]-NRT-code), using
(34, 68, large)-Net in Base 256 — Upper bound on s
There is no (34, 68, large)-net in base 256, because
- 32 times m-reduction [i] would yield (34, 36, large)-net in base 256, but