Best Known (67−34, 67, s)-Nets in Base 256
(67−34, 67, 3855)-Net over F256 — Constructive and digital
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
(67−34, 67, 10923)-Net over F256 — Digital
Digital (33, 67, 10923)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25667, 10923, F256, 6, 34) (dual of [(10923, 6), 65471, 35]-NRT-code), using
- OOA 6-folding [i] based on linear OA(25667, 65538, F256, 34) (dual of [65538, 65471, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [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(25665, 65536, F256, 33) (dual of [65536, 65471, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- OOA 6-folding [i] based on linear OA(25667, 65538, F256, 34) (dual of [65538, 65471, 35]-code), using
(67−34, 67, large)-Net in Base 256 — Upper bound on s
There is no (33, 67, large)-net in base 256, because
- 32 times m-reduction [i] would yield (33, 35, large)-net in base 256, but