Best Known (19, 19+13, s)-Nets in Base 256
(19, 19+13, 11180)-Net over F256 — Constructive and digital
Digital (19, 32, 11180)-net over F256, using
- net defined by OOA [i] based on linear OOA(25632, 11180, F256, 18, 13) (dual of [(11180, 18), 201208, 14]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25632, 11181, F256, 6, 13) (dual of [(11181, 6), 67054, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2567, 258, F256, 6, 6) (dual of [(258, 6), 1541, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2567, 258, F256, 5, 6) (dual of [(258, 5), 1283, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 7, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- extracting embedded OOA [i] based on digital (1, 7, 258)-net over F256, using
- appending kth column [i] based on linear OOA(2567, 258, F256, 5, 6) (dual of [(258, 5), 1283, 7]-NRT-code), using
- 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(2567, 258, F256, 6, 6) (dual of [(258, 6), 1541, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(25632, 11181, F256, 6, 13) (dual of [(11181, 6), 67054, 14]-NRT-code), using
(19, 19+13, 65827)-Net over F256 — Digital
Digital (19, 32, 65827)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25632, 65827, F256, 13) (dual of [65827, 65795, 14]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2567, 289, F256, 6) (dual of [289, 282, 7]-code), using
- extended algebraic-geometric code AGe(F,282P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- 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(2567, 289, F256, 6) (dual of [289, 282, 7]-code), using
- (u, u+v)-construction [i] based on
(19, 19+13, large)-Net in Base 256 — Upper bound on s
There is no (19, 32, large)-net in base 256, because
- 11 times m-reduction [i] would yield (19, 21, large)-net in base 256, but