Best Known (30, 30+21, s)-Nets in Base 256
(30, 30+21, 6810)-Net over F256 — Constructive and digital
Digital (30, 51, 6810)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (20, 41, 6553)-net over F256, using
- net defined by OOA [i] based on linear OOA(25641, 6553, F256, 21, 21) (dual of [(6553, 21), 137572, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25641, 65531, F256, 21) (dual of [65531, 65490, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25641, 65531, F256, 21) (dual of [65531, 65490, 22]-code), using
- net defined by OOA [i] based on linear OOA(25641, 6553, F256, 21, 21) (dual of [(6553, 21), 137572, 22]-NRT-code), using
- digital (0, 10, 257)-net over F256, using
(30, 30+21, 65795)-Net over F256 — Digital
Digital (30, 51, 65795)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25651, 65795, F256, 21) (dual of [65795, 65744, 22]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25610, 257, F256, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using
- extended Reed–Solomon code RSe(247,256) [i]
- algebraic-geometric code AG(F,123P) with 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,82P) 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 = 6 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25641, 65538, F256, 21) (dual of [65538, 65497, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(20) ⊂ Ce(19) [i] based on
- linear OA(25610, 257, F256, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using
- (u, u+v)-construction [i] based on
(30, 30+21, large)-Net in Base 256 — Upper bound on s
There is no (30, 51, large)-net in base 256, because
- 19 times m-reduction [i] would yield (30, 32, large)-net in base 256, but