Best Known (47−22, 47, s)-Nets in Base 256
(47−22, 47, 5959)-Net over F256 — Constructive and digital
Digital (25, 47, 5959)-net over F256, using
- net defined by OOA [i] based on linear OOA(25647, 5959, F256, 22, 22) (dual of [(5959, 22), 131051, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25647, 65549, F256, 22) (dual of [65549, 65502, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [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(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(25647, 65549, F256, 22) (dual of [65549, 65502, 23]-code), using
(47−22, 47, 21850)-Net over F256 — Digital
Digital (25, 47, 21850)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25647, 21850, F256, 3, 22) (dual of [(21850, 3), 65503, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [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(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- OOA 3-folding [i] based on linear OA(25647, 65550, F256, 22) (dual of [65550, 65503, 23]-code), using
(47−22, 47, large)-Net in Base 256 — Upper bound on s
There is no (25, 47, large)-net in base 256, because
- 20 times m-reduction [i] would yield (25, 27, large)-net in base 256, but