Best Known (51−7, 51, s)-Nets in Base 2
(51−7, 51, 65534)-Net over F2 — Constructive and digital
Digital (44, 51, 65534)-net over F2, using
- 21 times duplication [i] based on digital (43, 50, 65534)-net over F2, using
- net defined by OOA [i] based on linear OOA(250, 65534, F2, 7, 7) (dual of [(65534, 7), 458688, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(250, 65535, F2, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(250, 65534, F2, 7, 7) (dual of [(65534, 7), 458688, 8]-NRT-code), using
(51−7, 51, 65535)-Net over F2 — Digital
Digital (44, 51, 65535)-net over F2, using
- 21 times duplication [i] based on digital (43, 50, 65535)-net over F2, using
- net defined by OOA [i] based on linear OOA(250, 65535, F2, 7, 7) (dual of [(65535, 7), 458695, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(250, 65535, F2, 6, 7) (dual of [(65535, 6), 393160, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(250, 65535, F2, 3, 7) (dual of [(65535, 3), 196555, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(250, 65535, F2, 6, 7) (dual of [(65535, 6), 393160, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(250, 65535, F2, 7, 7) (dual of [(65535, 7), 458695, 8]-NRT-code), using
(51−7, 51, 189034)-Net in Base 2 — Upper bound on s
There is no (44, 51, 189035)-net in base 2, because
- 1 times m-reduction [i] would yield (44, 50, 189035)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1125 908202 645766 > 250 [i]