Best Known (46−19, 46, s)-Nets in Base 256
(46−19, 46, 7538)-Net over F256 — Constructive and digital
Digital (27, 46, 7538)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (18, 37, 7281)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- digital (0, 9, 257)-net over F256, using
(46−19, 46, 65795)-Net over F256 — Digital
Digital (27, 46, 65795)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25646, 65795, F256, 19) (dual of [65795, 65749, 20]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using
- extended Reed–Solomon code RSe(248,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+122P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- algebraic-geometric code AG(F, Q+81P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+49P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25637, 65538, F256, 19) (dual of [65538, 65501, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(2569, 257, F256, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using
- (u, u+v)-construction [i] based on
(46−19, 46, large)-Net in Base 256 — Upper bound on s
There is no (27, 46, large)-net in base 256, because
- 17 times m-reduction [i] would yield (27, 29, large)-net in base 256, but