Best Known (36−15, 36, s)-Nets in Base 256
(36−15, 36, 9619)-Net over F256 — Constructive and digital
Digital (21, 36, 9619)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (14, 29, 9362)-net over F256, using
- net defined by OOA [i] based on linear OOA(25629, 9362, F256, 15, 15) (dual of [(9362, 15), 140401, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25629, 65535, F256, 15) (dual of [65535, 65506, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25629, 65535, F256, 15) (dual of [65535, 65506, 16]-code), using
- net defined by OOA [i] based on linear OOA(25629, 9362, F256, 15, 15) (dual of [(9362, 15), 140401, 16]-NRT-code), using
- digital (0, 7, 257)-net over F256, using
(36−15, 36, 65795)-Net over F256 — Digital
Digital (21, 36, 65795)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25636, 65795, F256, 15) (dual of [65795, 65759, 16]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using
- extended Reed–Solomon code RSe(250,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+123P) 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,83P) with 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 = 4 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25629, 65538, F256, 15) (dual of [65538, 65509, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(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(14) ⊂ Ce(13) [i] based on
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using
- (u, u+v)-construction [i] based on
(36−15, 36, large)-Net in Base 256 — Upper bound on s
There is no (21, 36, large)-net in base 256, because
- 13 times m-reduction [i] would yield (21, 23, large)-net in base 256, but