Best Known (199−17, 199, s)-Nets in Base 2
(199−17, 199, 1048590)-Net over F2 — Constructive and digital
Digital (182, 199, 1048590)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 15)-net over F2, using
- digital (168, 185, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
(199−17, 199, 1398115)-Net over F2 — Digital
Digital (182, 199, 1398115)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2199, 1398115, F2, 6, 17) (dual of [(1398115, 6), 8388491, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(214, 15, F2, 6, 8) (dual of [(15, 6), 76, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 14, 15)-net over F2, using
- linear OOA(2185, 1398100, F2, 6, 17) (dual of [(1398100, 6), 8388415, 18]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(214, 15, F2, 6, 8) (dual of [(15, 6), 76, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(199−17, 199, large)-Net in Base 2 — Upper bound on s
There is no (182, 199, large)-net in base 2, because
- 15 times m-reduction [i] would yield (182, 184, large)-net in base 2, but