Best Known (56, 63, s)-Nets in Base 2
(56, 63, 1048574)-Net over F2 — Constructive and digital
Digital (56, 63, 1048574)-net over F2, using
- 21 times duplication [i] based on digital (55, 62, 1048574)-net over F2, using
- net defined by OOA [i] based on linear OOA(262, 1048574, F2, 7, 7) (dual of [(1048574, 7), 7339956, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(262, 1048575, F2, 3, 7) (dual of [(1048575, 3), 3145663, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(262, 1048574, F2, 7, 7) (dual of [(1048574, 7), 7339956, 8]-NRT-code), using
(56, 63, 1048575)-Net over F2 — Digital
Digital (56, 63, 1048575)-net over F2, using
- 21 times duplication [i] based on digital (55, 62, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(262, 1048575, F2, 7, 7) (dual of [(1048575, 7), 7339963, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(262, 1048575, F2, 6, 7) (dual of [(1048575, 6), 6291388, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(262, 1048575, F2, 3, 7) (dual of [(1048575, 3), 3145663, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(262, 1048575, F2, 6, 7) (dual of [(1048575, 6), 6291388, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(262, 1048575, F2, 7, 7) (dual of [(1048575, 7), 7339963, 8]-NRT-code), using
(56, 63, 3024612)-Net in Base 2 — Upper bound on s
There is no (56, 63, 3024613)-net in base 2, because
- 1 times m-reduction [i] would yield (56, 62, 3024613)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 4 611687 981327 337568 > 262 [i]