Best Known (20, 35, s)-Nets in Base 256
(20, 35, 9365)-Net over F256 — Constructive and digital
Digital (20, 35, 9365)-net over F256, using
- net defined by OOA [i] based on linear OOA(25635, 9365, F256, 15, 15) (dual of [(9365, 15), 140440, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25635, 65556, F256, 15) (dual of [65556, 65521, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(7) [i] based on
- 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(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(14) ⊂ Ce(7) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(25635, 65556, F256, 15) (dual of [65556, 65521, 16]-code), using
(20, 35, 44186)-Net over F256 — Digital
Digital (20, 35, 44186)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25635, 44186, F256, 15) (dual of [44186, 44151, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25635, 65544, F256, 15) (dual of [65544, 65509, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([1,7]) [i] based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25628, 65537, F256, 8) (dual of [65537, 65509, 9]-code), using the narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [1,7], and minimum distance d ≥ |{−7,−5,−3,…,7}|+1 = 9 (BCH-bound) [i]
- linear OA(2566, 7, F256, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,256)), using
- dual of repetition code with length 7 [i]
- construction X applied to C([0,7]) ⊂ C([1,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25635, 65544, F256, 15) (dual of [65544, 65509, 16]-code), using
(20, 35, large)-Net in Base 256 — Upper bound on s
There is no (20, 35, large)-net in base 256, because
- 13 times m-reduction [i] would yield (20, 22, large)-net in base 256, but