Best Known (34, 34+26, s)-Nets in Base 256
(34, 34+26, 5043)-Net over F256 — Constructive and digital
Digital (34, 60, 5043)-net over F256, using
- t-expansion [i] based on digital (33, 60, 5043)-net over F256, using
- net defined by OOA [i] based on linear OOA(25660, 5043, F256, 27, 27) (dual of [(5043, 27), 136101, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25660, 65560, F256, 27) (dual of [65560, 65500, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(25660, 65560, F256, 27) (dual of [65560, 65500, 28]-code), using
- net defined by OOA [i] based on linear OOA(25660, 5043, F256, 27, 27) (dual of [(5043, 27), 136101, 28]-NRT-code), using
(34, 34+26, 32782)-Net over F256 — Digital
Digital (34, 60, 32782)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25660, 32782, F256, 2, 26) (dual of [(32782, 2), 65504, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25660, 65564, F256, 26) (dual of [65564, 65504, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25660, 65565, F256, 26) (dual of [65565, 65505, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(15) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2569, 29, F256, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,256)), using
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- Reed–Solomon code RS(247,256) [i]
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- construction X applied to Ce(25) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(25660, 65565, F256, 26) (dual of [65565, 65505, 27]-code), using
- OOA 2-folding [i] based on linear OA(25660, 65564, F256, 26) (dual of [65564, 65504, 27]-code), using
(34, 34+26, large)-Net in Base 256 — Upper bound on s
There is no (34, 60, large)-net in base 256, because
- 24 times m-reduction [i] would yield (34, 36, large)-net in base 256, but