Best Known (158, 170, s)-Nets in Base 2
(158, 170, 1399122)-Net over F2 — Constructive and digital
Digital (158, 170, 1399122)-net over F2, using
- t-expansion [i] based on digital (157, 170, 1399122)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (25, 31, 1022)-net over F2, using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-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 (25, 31, 1022)-net over F2, using
- (u, u+v)-construction [i] based on
(158, 170, 2797224)-Net over F2 — Digital
Digital (158, 170, 2797224)-net over F2, using
- 21 times duplication [i] based on digital (157, 169, 2797224)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2169, 2797224, F2, 3, 12) (dual of [(2797224, 3), 8391503, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(231, 1023, F2, 3, 6) (dual of [(1023, 3), 3038, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(231, 1023, F2, 2, 6) (dual of [(1023, 2), 2015, 7]-NRT-code), using
- linear OOA(2138, 2796201, F2, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- linear OOA(231, 1023, F2, 3, 6) (dual of [(1023, 3), 3038, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2169, 2797224, F2, 3, 12) (dual of [(2797224, 3), 8391503, 13]-NRT-code), using
(158, 170, large)-Net in Base 2 — Upper bound on s
There is no (158, 170, large)-net in base 2, because
- 10 times m-reduction [i] would yield (158, 160, large)-net in base 2, but