Best Known (139, 139+13, s)-Nets in Base 2
(139, 139+13, 1398123)-Net over F2 — Constructive and digital
Digital (139, 152, 1398123)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (7, 13, 23)-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
(139, 139+13, 1677743)-Net over F2 — Digital
Digital (139, 152, 1677743)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, 1677743, F2, 5, 13) (dual of [(1677743, 5), 8388563, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(213, 23, F2, 5, 6) (dual of [(23, 5), 102, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 13, 23)-net over F2, using
- linear OOA(2139, 1677720, F2, 5, 13) (dual of [(1677720, 5), 8388461, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 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 5-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-code), using
- linear OOA(213, 23, F2, 5, 6) (dual of [(23, 5), 102, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(139, 139+13, large)-Net in Base 2 — Upper bound on s
There is no (139, 152, large)-net in base 2, because
- 11 times m-reduction [i] would yield (139, 141, large)-net in base 2, but