Best Known (32−12, 32, s)-Nets in Base 256
(32−12, 32, 11437)-Net over F256 — Constructive and digital
Digital (20, 32, 11437)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 514)-net over F256, using
- net defined by OOA [i] based on linear OOA(2569, 514, F256, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2569, 514, F256, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2563, 257, F256, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;1282,256) [i]
- linear OOA(2566, 257, F256, 5, 6) (dual of [(257, 5), 1279, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;1279,256) [i]
- linear OOA(2563, 257, F256, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2569, 514, F256, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2569, 514, F256, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), using
- digital (11, 23, 10923)-net over F256, using
- net defined by OOA [i] based on linear OOA(25623, 10923, F256, 12, 12) (dual of [(10923, 12), 131053, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(25623, 65538, F256, 12) (dual of [65538, 65515, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- 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(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(25623, 65538, F256, 12) (dual of [65538, 65515, 13]-code), using
- net defined by OOA [i] based on linear OOA(25623, 10923, F256, 12, 12) (dual of [(10923, 12), 131053, 13]-NRT-code), using
- digital (3, 9, 514)-net over F256, using
(32−12, 32, 195108)-Net over F256 — Digital
Digital (20, 32, 195108)-net over F256, using
(32−12, 32, large)-Net in Base 256 — Upper bound on s
There is no (20, 32, large)-net in base 256, because
- 10 times m-reduction [i] would yield (20, 22, large)-net in base 256, but