Best Known (13, 26, s)-Nets in Base 256
(13, 26, 10923)-Net over F256 — Constructive and digital
Digital (13, 26, 10923)-net over F256, using
- net defined by OOA [i] based on linear OOA(25626, 10923, F256, 13, 13) (dual of [(10923, 13), 141973, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25626, 65539, F256, 13) (dual of [65539, 65513, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25626, 65539, F256, 13) (dual of [65539, 65513, 14]-code), using
(13, 26, 21847)-Net over F256 — Digital
Digital (13, 26, 21847)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25626, 21847, F256, 3, 13) (dual of [(21847, 3), 65515, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25626, 65541, F256, 13) (dual of [65541, 65515, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25626, 65542, F256, 13) (dual of [65542, 65516, 14]-code), using
- OOA 3-folding [i] based on linear OA(25626, 65541, F256, 13) (dual of [65541, 65515, 14]-code), using
(13, 26, large)-Net in Base 256 — Upper bound on s
There is no (13, 26, large)-net in base 256, because
- 11 times m-reduction [i] would yield (13, 15, large)-net in base 256, but