Best Known (69−6, 69, s)-Nets in Base 2
(69−6, 69, 4194302)-Net over F2 — Constructive and digital
Digital (63, 69, 4194302)-net over F2, using
- 21 times duplication [i] based on digital (62, 68, 4194302)-net over F2, using
- net defined by OOA [i] based on linear OOA(268, 4194302, F2, 6, 6) (dual of [(4194302, 6), 25165744, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(268, 4194303, F2, 3, 6) (dual of [(4194303, 3), 12582841, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(268, 4194303, F2, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(268, 4194303, F2, 3, 6) (dual of [(4194303, 3), 12582841, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(268, 4194302, F2, 6, 6) (dual of [(4194302, 6), 25165744, 7]-NRT-code), using
(69−6, 69, 4194304)-Net over F2 — Digital
Digital (63, 69, 4194304)-net over F2, using
- net defined by OOA [i] based on linear OOA(269, 4194304, F2, 6, 6) (dual of [(4194304, 6), 25165755, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(269, 4194304, F2, 5, 6) (dual of [(4194304, 5), 20971451, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(269, 4194304, F2, 2, 6) (dual of [(4194304, 2), 8388539, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(267, 4194303, F2, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(269, 4194304, F2, 2, 6) (dual of [(4194304, 2), 8388539, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(269, 4194304, F2, 5, 6) (dual of [(4194304, 5), 20971451, 7]-NRT-code), using
(69−6, 69, large)-Net in Base 2 — Upper bound on s
There is no (63, 69, large)-net in base 2, because
- 4 times m-reduction [i] would yield (63, 65, large)-net in base 2, but