Best Known (199−13, 199, s)-Nets in Base 2
(199−13, 199, 1922387)-Net over F2 — Constructive and digital
Digital (186, 199, 1922387)-net over F2, using
- 22 times duplication [i] based on digital (184, 197, 1922387)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (52, 58, 524287)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 59, 524287)-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 (52, 58, 524287)-net over F2, using
- (u, u+v)-construction [i] based on
(199−13, 199, 3857142)-Net over F2 — Digital
Digital (186, 199, 3857142)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2199, 3857142, F2, 2, 13) (dual of [(3857142, 2), 7714085, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2199, 4718589, F2, 2, 13) (dual of [(4718589, 2), 9436979, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2197, 4718588, F2, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(258, 524287, F2, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 59, 524287)-net over F2, using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, 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
- linear OOA(258, 524287, F2, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2197, 4718588, F2, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2199, 4718589, F2, 2, 13) (dual of [(4718589, 2), 9436979, 14]-NRT-code), using
(199−13, 199, large)-Net in Base 2 — Upper bound on s
There is no (186, 199, large)-net in base 2, because
- 11 times m-reduction [i] would yield (186, 188, large)-net in base 2, but