Best Known (32, 32+23, s)-Nets in Base 256
(32, 32+23, 5960)-Net over F256 — Constructive and digital
Digital (32, 55, 5960)-net over F256, using
- 2562 times duplication [i] based on digital (30, 53, 5960)-net over F256, using
- net defined by OOA [i] based on linear OOA(25653, 5960, F256, 23, 23) (dual of [(5960, 23), 137027, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25653, 65561, F256, 23) (dual of [65561, 65508, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(13) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(22) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(25653, 65562, F256, 23) (dual of [65562, 65509, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25653, 65561, F256, 23) (dual of [65561, 65508, 24]-code), using
- net defined by OOA [i] based on linear OOA(25653, 5960, F256, 23, 23) (dual of [(5960, 23), 137027, 24]-NRT-code), using
(32, 32+23, 53026)-Net over F256 — Digital
Digital (32, 55, 53026)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25655, 53026, F256, 23) (dual of [53026, 52971, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25655, 65548, F256, 23) (dual of [65548, 65493, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([1,11]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25644, 65537, F256, 12) (dual of [65537, 65493, 13]-code), using the narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [1,11], and minimum distance d ≥ |{−11,−9,−7,…,11}|+1 = 13 (BCH-bound) [i]
- linear OA(25610, 11, F256, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,256)), using
- dual of repetition code with length 11 [i]
- construction X applied to C([0,11]) ⊂ C([1,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25655, 65548, F256, 23) (dual of [65548, 65493, 24]-code), using
(32, 32+23, large)-Net in Base 256 — Upper bound on s
There is no (32, 55, large)-net in base 256, because
- 21 times m-reduction [i] would yield (32, 34, large)-net in base 256, but