Best Known (60, 67, s)-Nets in Base 2
(60, 67, 2097150)-Net over F2 — Constructive and digital
Digital (60, 67, 2097150)-net over F2, using
- 22 times duplication [i] based on digital (58, 65, 2097150)-net over F2, using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(265, 2097151, F2, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
(60, 67, 2097151)-Net over F2 — Digital
Digital (60, 67, 2097151)-net over F2, using
- 22 times duplication [i] based on digital (58, 65, 2097151)-net over F2, using
- net defined by OOA [i] based on linear OOA(265, 2097151, F2, 7, 7) (dual of [(2097151, 7), 14679992, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(265, 2097151, F2, 6, 7) (dual of [(2097151, 6), 12582841, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(265, 2097151, F2, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(265, 2097151, F2, 6, 7) (dual of [(2097151, 6), 12582841, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(265, 2097151, F2, 7, 7) (dual of [(2097151, 7), 14679992, 8]-NRT-code), using
(60, 67, 7621552)-Net in Base 2 — Upper bound on s
There is no (60, 67, 7621553)-net in base 2, because
- 1 times m-reduction [i] would yield (60, 66, 7621553)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 73 787000 372393 647688 > 266 [i]