Best Known (34, 34+28, s)-Nets in Base 256
(34, 34+28, 4682)-Net over F256 — Constructive and digital
Digital (34, 62, 4682)-net over F256, using
- 2561 times duplication [i] based on digital (33, 61, 4682)-net over F256, using
- t-expansion [i] based on digital (32, 61, 4682)-net over F256, using
- net defined by OOA [i] based on linear OOA(25661, 4682, F256, 29, 29) (dual of [(4682, 29), 135717, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25661, 65549, F256, 29) (dual of [65549, 65488, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25661, 65550, F256, 29) (dual of [65550, 65489, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(25661, 65550, F256, 29) (dual of [65550, 65489, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25661, 65549, F256, 29) (dual of [65549, 65488, 30]-code), using
- net defined by OOA [i] based on linear OOA(25661, 4682, F256, 29, 29) (dual of [(4682, 29), 135717, 30]-NRT-code), using
- t-expansion [i] based on digital (32, 61, 4682)-net over F256, using
(34, 34+28, 24024)-Net over F256 — Digital
Digital (34, 62, 24024)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25662, 24024, F256, 2, 28) (dual of [(24024, 2), 47986, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25662, 32779, F256, 2, 28) (dual of [(32779, 2), 65496, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25662, 65558, F256, 28) (dual of [65558, 65496, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25662, 65559, F256, 28) (dual of [65559, 65497, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(25662, 65559, F256, 28) (dual of [65559, 65497, 29]-code), using
- OOA 2-folding [i] based on linear OA(25662, 65558, F256, 28) (dual of [65558, 65496, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(25662, 32779, F256, 2, 28) (dual of [(32779, 2), 65496, 29]-NRT-code), using
(34, 34+28, large)-Net in Base 256 — Upper bound on s
There is no (34, 62, large)-net in base 256, because
- 26 times m-reduction [i] would yield (34, 36, large)-net in base 256, but