Best Known (54, 60, s)-Nets in Base 2
(54, 60, 524287)-Net over F2 — Constructive and digital
Digital (54, 60, 524287)-net over F2, using
- 21 times duplication [i] based on digital (53, 59, 524287)-net over F2, using
- t-expansion [i] based on digital (52, 59, 524287)-net over F2, using
(54, 60, 524288)-Net over F2 — Digital
Digital (54, 60, 524288)-net over F2, using
- net defined by OOA [i] based on linear OOA(260, 524288, F2, 6, 6) (dual of [(524288, 6), 3145668, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(260, 524288, F2, 5, 6) (dual of [(524288, 5), 2621380, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(260, 524288, F2, 2, 6) (dual of [(524288, 2), 1048516, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(258, 524287, F2, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(260, 524288, F2, 2, 6) (dual of [(524288, 2), 1048516, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(260, 524288, F2, 5, 6) (dual of [(524288, 5), 2621380, 7]-NRT-code), using
(54, 60, 1905385)-Net in Base 2 — Upper bound on s
There is no (54, 60, 1905386)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 152923 242254 102768 > 260 [i]