Best Known (24, 24+20, s)-Nets in Base 256
(24, 24+20, 6555)-Net over F256 — Constructive and digital
Digital (24, 44, 6555)-net over F256, using
- 2561 times duplication [i] based on digital (23, 43, 6555)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 6555, F256, 20, 20) (dual of [(6555, 20), 131057, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25643, 65550, F256, 20) (dual of [65550, 65507, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(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(19) ⊂ Ce(14) [i] based on
- OA 10-folding and stacking [i] based on linear OA(25643, 65550, F256, 20) (dual of [65550, 65507, 21]-code), using
- net defined by OOA [i] based on linear OOA(25643, 6555, F256, 20, 20) (dual of [(6555, 20), 131057, 21]-NRT-code), using
(24, 24+20, 25064)-Net over F256 — Digital
Digital (24, 44, 25064)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25644, 25064, F256, 2, 20) (dual of [(25064, 2), 50084, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25644, 32776, F256, 2, 20) (dual of [(32776, 2), 65508, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25644, 65552, F256, 20) (dual of [65552, 65508, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25644, 65553, F256, 20) (dual of [65553, 65509, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(25644, 65553, F256, 20) (dual of [65553, 65509, 21]-code), using
- OOA 2-folding [i] based on linear OA(25644, 65552, F256, 20) (dual of [65552, 65508, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(25644, 32776, F256, 2, 20) (dual of [(32776, 2), 65508, 21]-NRT-code), using
(24, 24+20, large)-Net in Base 256 — Upper bound on s
There is no (24, 44, large)-net in base 256, because
- 18 times m-reduction [i] would yield (24, 26, large)-net in base 256, but