Best Known (22, 22+16, s)-Nets in Base 256
(22, 22+16, 8194)-Net over F256 — Constructive and digital
Digital (22, 38, 8194)-net over F256, using
- t-expansion [i] based on digital (21, 38, 8194)-net over F256, using
- net defined by OOA [i] based on linear OOA(25638, 8194, F256, 17, 17) (dual of [(8194, 17), 139260, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25638, 65553, F256, 17) (dual of [65553, 65515, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(25638, 65554, F256, 17) (dual of [65554, 65516, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [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]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25638, 65554, F256, 17) (dual of [65554, 65516, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25638, 65553, F256, 17) (dual of [65553, 65515, 18]-code), using
- net defined by OOA [i] based on linear OOA(25638, 8194, F256, 17, 17) (dual of [(8194, 17), 139260, 18]-NRT-code), using
(22, 22+16, 54891)-Net over F256 — Digital
Digital (22, 38, 54891)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25638, 54891, F256, 16) (dual of [54891, 54853, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25638, 65559, F256, 16) (dual of [65559, 65521, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(7) [i] based on
- 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(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(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 Ce(15) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(25638, 65559, F256, 16) (dual of [65559, 65521, 17]-code), using
(22, 22+16, large)-Net in Base 256 — Upper bound on s
There is no (22, 38, large)-net in base 256, because
- 14 times m-reduction [i] would yield (22, 24, large)-net in base 256, but