Best Known (61−28, 61, s)-Nets in Base 256
(61−28, 61, 4682)-Net over F256 — Constructive and digital
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
(61−28, 61, 21852)-Net over F256 — Digital
Digital (33, 61, 21852)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25661, 21852, F256, 3, 28) (dual of [(21852, 3), 65495, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25661, 65556, F256, 28) (dual of [65556, 65495, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [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(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- OOA 3-folding [i] based on linear OA(25661, 65556, F256, 28) (dual of [65556, 65495, 29]-code), using
(61−28, 61, large)-Net in Base 256 — Upper bound on s
There is no (33, 61, large)-net in base 256, because
- 26 times m-reduction [i] would yield (33, 35, large)-net in base 256, but