Best Known (35, 35+25, s)-Nets in Base 256
(35, 35+25, 5464)-Net over F256 — Constructive and digital
Digital (35, 60, 5464)-net over F256, using
- net defined by OOA [i] based on linear OOA(25660, 5464, F256, 25, 25) (dual of [(5464, 25), 136540, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25660, 65569, F256, 25) (dual of [65569, 65509, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(25660, 65572, F256, 25) (dual of [65572, 65512, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,6]) [i] based on
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(25611, 35, F256, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,256)), using
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- Reed–Solomon code RS(245,256) [i]
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- construction X applied to C([0,12]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25660, 65572, F256, 25) (dual of [65572, 65512, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25660, 65569, F256, 25) (dual of [65569, 65509, 26]-code), using
(35, 35+25, 55654)-Net over F256 — Digital
Digital (35, 60, 55654)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25660, 55654, F256, 25) (dual of [55654, 55594, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(25660, 65572, F256, 25) (dual of [65572, 65512, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,6]) [i] based on
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(25611, 35, F256, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,256)), using
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- Reed–Solomon code RS(245,256) [i]
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- construction X applied to C([0,12]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25660, 65572, F256, 25) (dual of [65572, 65512, 26]-code), using
(35, 35+25, large)-Net in Base 256 — Upper bound on s
There is no (35, 60, large)-net in base 256, because
- 23 times m-reduction [i] would yield (35, 37, large)-net in base 256, but