Best Known (18, 35, s)-Nets in Base 256
(18, 35, 8192)-Net over F256 — Constructive and digital
Digital (18, 35, 8192)-net over F256, using
- 2562 times duplication [i] based on digital (16, 33, 8192)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
(18, 35, 18824)-Net over F256 — Digital
Digital (18, 35, 18824)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25635, 18824, F256, 3, 17) (dual of [(18824, 3), 56437, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25635, 21848, F256, 3, 17) (dual of [(21848, 3), 65509, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25635, 65544, F256, 17) (dual of [65544, 65509, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- OOA 3-folding [i] based on linear OA(25635, 65544, F256, 17) (dual of [65544, 65509, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(25635, 21848, F256, 3, 17) (dual of [(21848, 3), 65509, 18]-NRT-code), using
(18, 35, large)-Net in Base 256 — Upper bound on s
There is no (18, 35, large)-net in base 256, because
- 15 times m-reduction [i] would yield (18, 20, large)-net in base 256, but