Best Known (63−6, 63, s)-Nets in Base 2
(63−6, 63, 1048574)-Net over F2 — Constructive and digital
Digital (57, 63, 1048574)-net over F2, using
- 21 times duplication [i] based on digital (56, 62, 1048574)-net over F2, using
- net defined by OOA [i] based on linear OOA(262, 1048574, F2, 6, 6) (dual of [(1048574, 6), 6291382, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(262, 1048575, F2, 3, 6) (dual of [(1048575, 3), 3145663, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(262, 1048575, F2, 3, 7) (dual of [(1048575, 3), 3145663, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(262, 1048575, F2, 3, 6) (dual of [(1048575, 3), 3145663, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(262, 1048574, F2, 6, 6) (dual of [(1048574, 6), 6291382, 7]-NRT-code), using
(63−6, 63, 1048576)-Net over F2 — Digital
Digital (57, 63, 1048576)-net over F2, using
- net defined by OOA [i] based on linear OOA(263, 1048576, F2, 6, 6) (dual of [(1048576, 6), 6291393, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(263, 1048576, F2, 5, 6) (dual of [(1048576, 5), 5242817, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(263, 1048576, F2, 2, 6) (dual of [(1048576, 2), 2097089, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(261, 1048575, F2, 2, 6) (dual of [(1048575, 2), 2097089, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(263, 1048576, F2, 2, 6) (dual of [(1048576, 2), 2097089, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(263, 1048576, F2, 5, 6) (dual of [(1048576, 5), 5242817, 7]-NRT-code), using
(63−6, 63, 3810774)-Net in Base 2 — Upper bound on s
There is no (57, 63, 3810775)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 9 223378 677048 825726 > 263 [i]