Best Known (33−13, 33, s)-Nets in Base 256
(33−13, 33, 11181)-Net over F256 — Constructive and digital
Digital (20, 33, 11181)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 11181, F256, 18, 13) (dual of [(11181, 18), 201225, 14]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25633, 11182, F256, 6, 13) (dual of [(11182, 6), 67059, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2568, 259, F256, 6, 6) (dual of [(259, 6), 1546, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2568, 259, F256, 5, 6) (dual of [(259, 5), 1287, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 8, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- extracting embedded OOA [i] based on digital (2, 8, 259)-net over F256, using
- appending kth column [i] based on linear OOA(2568, 259, F256, 5, 6) (dual of [(259, 5), 1287, 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(2568, 259, F256, 6, 6) (dual of [(259, 6), 1546, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(25633, 11182, F256, 6, 13) (dual of [(11182, 6), 67059, 14]-NRT-code), using
(33−13, 33, 86998)-Net over F256 — Digital
Digital (20, 33, 86998)-net over F256, using
(33−13, 33, large)-Net in Base 256 — Upper bound on s
There is no (20, 33, large)-net in base 256, because
- 11 times m-reduction [i] would yield (20, 22, large)-net in base 256, but