Best Known (24, 42, s)-Nets in Base 256
(24, 42, 7284)-Net over F256 — Constructive and digital
Digital (24, 42, 7284)-net over F256, using
- 2561 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(25641, 7284, F256, 18, 18) (dual of [(7284, 18), 131071, 19]-NRT-code), using
(24, 42, 39540)-Net over F256 — Digital
Digital (24, 42, 39540)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25642, 39540, F256, 18) (dual of [39540, 39498, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25642, 65559, F256, 18) (dual of [65559, 65517, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(9) [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(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to Ce(17) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(25642, 65559, F256, 18) (dual of [65559, 65517, 19]-code), using
(24, 42, large)-Net in Base 256 — Upper bound on s
There is no (24, 42, large)-net in base 256, because
- 16 times m-reduction [i] would yield (24, 26, large)-net in base 256, but