Best Known (23, 23+18, s)-Nets in Base 256
(23, 23+18, 7284)-Net over F256 — Constructive and digital
Digital (23, 41, 7284)-net over F256, using
- net defined by OOA [i] based on linear OOA(25641, 7284, F256, 18, 18) (dual of [(7284, 18), 131071, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25641, 65556, F256, 18) (dual of [65556, 65515, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- 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(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(17) ⊂ Ce(10) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25641, 65556, F256, 18) (dual of [65556, 65515, 19]-code), using
(23, 23+18, 32778)-Net over F256 — Digital
Digital (23, 41, 32778)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25641, 32778, F256, 2, 18) (dual of [(32778, 2), 65515, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25641, 65556, F256, 18) (dual of [65556, 65515, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- 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(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(17) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(25641, 65556, F256, 18) (dual of [65556, 65515, 19]-code), using
(23, 23+18, large)-Net in Base 256 — Upper bound on s
There is no (23, 41, large)-net in base 256, because
- 16 times m-reduction [i] would yield (23, 25, large)-net in base 256, but