Best Known (69−7, 69, s)-Nets in Base 2
(69−7, 69, 4194302)-Net over F2 — Constructive and digital
Digital (62, 69, 4194302)-net over F2, using
- 21 times duplication [i] based on digital (61, 68, 4194302)-net over F2, using
- net defined by OOA [i] based on linear OOA(268, 4194302, F2, 7, 7) (dual of [(4194302, 7), 29360046, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(268, 4194303, F2, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(268, 4194302, F2, 7, 7) (dual of [(4194302, 7), 29360046, 8]-NRT-code), using
(69−7, 69, 4194303)-Net over F2 — Digital
Digital (62, 69, 4194303)-net over F2, using
- 21 times duplication [i] based on digital (61, 68, 4194303)-net over F2, using
- net defined by OOA [i] based on linear OOA(268, 4194303, F2, 7, 7) (dual of [(4194303, 7), 29360053, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(268, 4194303, F2, 6, 7) (dual of [(4194303, 6), 25165750, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(268, 4194303, F2, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(268, 4194303, F2, 6, 7) (dual of [(4194303, 6), 25165750, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(268, 4194303, F2, 7, 7) (dual of [(4194303, 7), 29360053, 8]-NRT-code), using
(69−7, 69, large)-Net in Base 2 — Upper bound on s
There is no (62, 69, large)-net in base 2, because
- 5 times m-reduction [i] would yield (62, 64, large)-net in base 2, but