Best Known (205−13, 205, s)-Nets in Base 2
(205−13, 205, 2796200)-Net over F2 — Constructive and digital
Digital (192, 205, 2796200)-net over F2, using
- 22 times duplication [i] based on digital (190, 203, 2796200)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (58, 64, 2097150)-net over F2, using
- 1 times m-reduction [i] based on digital (58, 65, 2097150)-net over F2, using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(265, 2097151, F2, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- 1 times m-reduction [i] based on digital (58, 65, 2097150)-net over F2, using
- digital (126, 139, 1398100)-net over F2, using
- net defined by OOA [i] based on linear OOA(2139, 1398100, F2, 13, 13) (dual of [(1398100, 13), 18175161, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-code), using
- net defined by OOA [i] based on linear OOA(2139, 1398100, F2, 13, 13) (dual of [(1398100, 13), 18175161, 14]-NRT-code), using
- digital (58, 64, 2097150)-net over F2, using
- (u, u+v)-construction [i] based on
(205−13, 205, 5846341)-Net over F2 — Digital
Digital (192, 205, 5846341)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2205, 5846341, F2, 2, 13) (dual of [(5846341, 2), 11692477, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2205, 6291453, F2, 2, 13) (dual of [(6291453, 2), 12582701, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2203, 6291452, F2, 2, 13) (dual of [(6291452, 2), 12582701, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(264, 2097151, F2, 2, 6) (dual of [(2097151, 2), 4194238, 7]-NRT-code), using
- linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2203, 6291452, F2, 2, 13) (dual of [(6291452, 2), 12582701, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2205, 6291453, F2, 2, 13) (dual of [(6291453, 2), 12582701, 14]-NRT-code), using
(205−13, 205, large)-Net in Base 2 — Upper bound on s
There is no (192, 205, large)-net in base 2, because
- 11 times m-reduction [i] would yield (192, 194, large)-net in base 2, but