Best Known (49−21, 49, s)-Nets in Base 256
(49−21, 49, 6556)-Net over F256 — Constructive and digital
Digital (28, 49, 6556)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 6556, F256, 21, 21) (dual of [(6556, 21), 137627, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25649, 65561, F256, 21) (dual of [65561, 65512, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, 65562, F256, 21) (dual of [65562, 65513, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(11) [i] based on
- 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(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(20) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(25649, 65562, F256, 21) (dual of [65562, 65513, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25649, 65561, F256, 21) (dual of [65561, 65512, 22]-code), using
(49−21, 49, 37718)-Net over F256 — Digital
Digital (28, 49, 37718)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25649, 37718, F256, 21) (dual of [37718, 37669, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, 65562, F256, 21) (dual of [65562, 65513, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(11) [i] based on
- 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(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(20) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(25649, 65562, F256, 21) (dual of [65562, 65513, 22]-code), using
(49−21, 49, large)-Net in Base 256 — Upper bound on s
There is no (28, 49, large)-net in base 256, because
- 19 times m-reduction [i] would yield (28, 30, large)-net in base 256, but