Best Known (66−6, 66, s)-Nets in Base 2
(66−6, 66, 2097150)-Net over F2 — Constructive and digital
Digital (60, 66, 2097150)-net over F2, using
- 21 times duplication [i] based on digital (59, 65, 2097150)-net over F2, using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 6, 6) (dual of [(2097150, 6), 12582835, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(265, 2097151, F2, 3, 6) (dual of [(2097151, 3), 6291388, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(265, 2097151, F2, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(265, 2097151, F2, 3, 6) (dual of [(2097151, 3), 6291388, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 6, 6) (dual of [(2097150, 6), 12582835, 7]-NRT-code), using
(66−6, 66, 2097152)-Net over F2 — Digital
Digital (60, 66, 2097152)-net over F2, using
- net defined by OOA [i] based on linear OOA(266, 2097152, F2, 6, 6) (dual of [(2097152, 6), 12582846, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(266, 2097152, F2, 5, 6) (dual of [(2097152, 5), 10485694, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(266, 2097152, F2, 2, 6) (dual of [(2097152, 2), 4194238, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(264, 2097151, F2, 2, 6) (dual of [(2097151, 2), 4194238, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(266, 2097152, F2, 2, 6) (dual of [(2097152, 2), 4194238, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(266, 2097152, F2, 5, 6) (dual of [(2097152, 5), 10485694, 7]-NRT-code), using
(66−6, 66, 7621552)-Net in Base 2 — Upper bound on s
There is no (60, 66, 7621553)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 73 787000 372393 647688 > 266 [i]