Best Known (47−19, 47, s)-Nets in Base 256
(47−19, 47, 7539)-Net over F256 — Constructive and digital
Digital (28, 47, 7539)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (18, 37, 7281)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25637, 65530, F256, 19) (dual of [65530, 65493, 20]-code), using
- net defined by OOA [i] based on linear OOA(25637, 7281, F256, 19, 19) (dual of [(7281, 19), 138302, 20]-NRT-code), using
- digital (1, 10, 258)-net over F256, using
(47−19, 47, 65827)-Net over F256 — Digital
Digital (28, 47, 65827)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25647, 65827, F256, 19) (dual of [65827, 65780, 20]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25610, 289, F256, 9) (dual of [289, 279, 10]-code), using
- extended algebraic-geometric code AGe(F,279P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- linear OA(25637, 65538, F256, 19) (dual of [65538, 65501, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- linear OA(25610, 289, F256, 9) (dual of [289, 279, 10]-code), using
- (u, u+v)-construction [i] based on
(47−19, 47, large)-Net in Base 256 — Upper bound on s
There is no (28, 47, large)-net in base 256, because
- 17 times m-reduction [i] would yield (28, 30, large)-net in base 256, but