Best Known (18, 31, s)-Nets in Base 256
(18, 31, 11179)-Net over F256 — Constructive and digital
Digital (18, 31, 11179)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 11179, F256, 18, 13) (dual of [(11179, 18), 201191, 14]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25631, 11180, F256, 6, 13) (dual of [(11180, 6), 67049, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2566, 257, F256, 6, 6) (dual of [(257, 6), 1536, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1536,256) [i]
- linear OOA(25625, 10923, F256, 6, 13) (dual of [(10923, 6), 65513, 14]-NRT-code), using
- OOA 6-folding [i] based on linear OA(25625, 65538, F256, 13) (dual of [65538, 65513, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- OOA 6-folding [i] based on linear OA(25625, 65538, F256, 13) (dual of [65538, 65513, 14]-code), using
- linear OOA(2566, 257, F256, 6, 6) (dual of [(257, 6), 1536, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(25631, 11180, F256, 6, 13) (dual of [(11180, 6), 67049, 14]-NRT-code), using
(18, 31, 65795)-Net over F256 — Digital
Digital (18, 31, 65795)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25631, 65795, F256, 13) (dual of [65795, 65764, 14]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2566, 257, F256, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using
- extended Reed–Solomon code RSe(251,256) [i]
- algebraic-geometric code AG(F,125P) 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, Q+82P) 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,50P) with degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(25625, 65538, F256, 13) (dual of [65538, 65513, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- linear OA(2566, 257, F256, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using
- (u, u+v)-construction [i] based on
(18, 31, large)-Net in Base 256 — Upper bound on s
There is no (18, 31, large)-net in base 256, because
- 11 times m-reduction [i] would yield (18, 20, large)-net in base 256, but