Best Known (45−7, 45, s)-Nets in Base 2
(45−7, 45, 16382)-Net over F2 — Constructive and digital
Digital (38, 45, 16382)-net over F2, using
- 21 times duplication [i] based on digital (37, 44, 16382)-net over F2, using
- net defined by OOA [i] based on linear OOA(244, 16382, F2, 7, 7) (dual of [(16382, 7), 114630, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(244, 16383, F2, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(244, 16382, F2, 7, 7) (dual of [(16382, 7), 114630, 8]-NRT-code), using
(45−7, 45, 16383)-Net over F2 — Digital
Digital (38, 45, 16383)-net over F2, using
- 21 times duplication [i] based on digital (37, 44, 16383)-net over F2, using
- net defined by OOA [i] based on linear OOA(244, 16383, F2, 7, 7) (dual of [(16383, 7), 114637, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(244, 16383, F2, 6, 7) (dual of [(16383, 6), 98254, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(244, 16383, F2, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(244, 16383, F2, 6, 7) (dual of [(16383, 6), 98254, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(244, 16383, F2, 7, 7) (dual of [(16383, 7), 114637, 8]-NRT-code), using
(45−7, 45, 47255)-Net in Base 2 — Upper bound on s
There is no (38, 45, 47256)-net in base 2, because
- 1 times m-reduction [i] would yield (38, 44, 47256)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 17 592594 713013 > 244 [i]