Best Known (162, 174, s)-Nets in Base 2
(162, 174, 1400147)-Net over F2 — Constructive and digital
Digital (162, 174, 1400147)-net over F2, using
- 21 times duplication [i] based on digital (161, 173, 1400147)-net over F2, using
- t-expansion [i] based on digital (160, 173, 1400147)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (28, 34, 2047)-net over F2, using
- 1 times m-reduction [i] based on digital (28, 35, 2047)-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 (28, 34, 2047)-net over F2, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (160, 173, 1400147)-net over F2, using
(162, 174, 2798249)-Net over F2 — Digital
Digital (162, 174, 2798249)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2174, 2798249, F2, 3, 12) (dual of [(2798249, 3), 8394573, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(236, 2048, F2, 3, 6) (dual of [(2048, 3), 6108, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 2048, F2, 2, 6) (dual of [(2048, 2), 4060, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(234, 2047, F2, 2, 6) (dual of [(2047, 2), 4060, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F2, using
- 1 times m-reduction [i] based on digital (28, 35, 2047)-net over F2, using
- extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F2, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(234, 2047, F2, 2, 6) (dual of [(2047, 2), 4060, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 2048, F2, 2, 6) (dual of [(2048, 2), 4060, 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(236, 2048, F2, 3, 6) (dual of [(2048, 3), 6108, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(162, 174, large)-Net in Base 2 — Upper bound on s
There is no (162, 174, large)-net in base 2, because
- 10 times m-reduction [i] would yield (162, 164, large)-net in base 2, but