Best Known (38, 38+26, s)-Nets in Base 256
(38, 38+26, 5298)-Net over F256 — Constructive and digital
Digital (38, 64, 5298)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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 (25, 51, 5041)-net over F256, using
- net defined by OOA [i] based on linear OOA(25651, 5041, F256, 26, 26) (dual of [(5041, 26), 131015, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25651, 65533, F256, 26) (dual of [65533, 65482, 27]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25651, 65533, F256, 26) (dual of [65533, 65482, 27]-code), using
- net defined by OOA [i] based on linear OOA(25651, 5041, F256, 26, 26) (dual of [(5041, 26), 131015, 27]-NRT-code), using
- digital (0, 13, 257)-net over F256, using
(38, 38+26, 65795)-Net over F256 — Digital
Digital (38, 64, 65795)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25664, 65795, F256, 26) (dual of [65795, 65731, 27]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25613, 257, F256, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using
- extended Reed–Solomon code RSe(244,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+120P) 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,81P) 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+48P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25651, 65538, F256, 26) (dual of [65538, 65487, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [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(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- linear OA(25613, 257, F256, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using
- (u, u+v)-construction [i] based on
(38, 38+26, large)-Net in Base 256 — Upper bound on s
There is no (38, 64, large)-net in base 256, because
- 24 times m-reduction [i] would yield (38, 40, large)-net in base 256, but