Best Known (27, 49, s)-Nets in Base 256
(27, 49, 5959)-Net over F256 — Constructive and digital
Digital (27, 49, 5959)-net over F256, using
- t-expansion [i] based on digital (26, 49, 5959)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5959, F256, 23, 23) (dual of [(5959, 23), 137008, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25649, 65550, F256, 23) (dual of [65550, 65501, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(22) ⊂ Ce(17) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(25649, 65550, F256, 23) (dual of [65550, 65501, 24]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5959, F256, 23, 23) (dual of [(5959, 23), 137008, 24]-NRT-code), using
(27, 49, 28169)-Net over F256 — Digital
Digital (27, 49, 28169)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25649, 28169, F256, 2, 22) (dual of [(28169, 2), 56289, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25649, 32778, F256, 2, 22) (dual of [(32778, 2), 65507, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25649, 65556, F256, 22) (dual of [65556, 65507, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(21) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(25649, 65556, F256, 22) (dual of [65556, 65507, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(25649, 32778, F256, 2, 22) (dual of [(32778, 2), 65507, 23]-NRT-code), using
(27, 49, large)-Net in Base 256 — Upper bound on s
There is no (27, 49, large)-net in base 256, because
- 20 times m-reduction [i] would yield (27, 29, large)-net in base 256, but