Best Known (36, 42, s)-Nets in Base 2
(36, 42, 8191)-Net over F2 — Constructive and digital
Digital (36, 42, 8191)-net over F2, using
- 21 times duplication [i] based on digital (35, 41, 8191)-net over F2, using
- t-expansion [i] based on digital (34, 41, 8191)-net over F2, using
(36, 42, 8192)-Net over F2 — Digital
Digital (36, 42, 8192)-net over F2, using
- net defined by OOA [i] based on linear OOA(242, 8192, F2, 6, 6) (dual of [(8192, 6), 49110, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(242, 8192, F2, 5, 6) (dual of [(8192, 5), 40918, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(242, 8192, F2, 2, 6) (dual of [(8192, 2), 16342, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(240, 8191, F2, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- 1 times m-reduction [i] based on digital (34, 41, 8191)-net over F2, using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(240, 8191, F2, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(242, 8192, F2, 2, 6) (dual of [(8192, 2), 16342, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(242, 8192, F2, 5, 6) (dual of [(8192, 5), 40918, 7]-NRT-code), using
(36, 42, 29767)-Net in Base 2 — Upper bound on s
There is no (36, 42, 29768)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 4 398177 690333 > 242 [i]