Best Known (49−7, 49, s)-Nets in Base 2
(49−7, 49, 32766)-Net over F2 — Constructive and digital
Digital (42, 49, 32766)-net over F2, using
- 22 times duplication [i] based on digital (40, 47, 32766)-net over F2, using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 7, 7) (dual of [(32766, 7), 229315, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(247, 32767, F2, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 7, 7) (dual of [(32766, 7), 229315, 8]-NRT-code), using
(49−7, 49, 32767)-Net over F2 — Digital
Digital (42, 49, 32767)-net over F2, using
- 22 times duplication [i] based on digital (40, 47, 32767)-net over F2, using
- net defined by OOA [i] based on linear OOA(247, 32767, F2, 7, 7) (dual of [(32767, 7), 229322, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(247, 32767, F2, 6, 7) (dual of [(32767, 6), 196555, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(247, 32767, F2, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(247, 32767, F2, 6, 7) (dual of [(32767, 6), 196555, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(247, 32767, F2, 7, 7) (dual of [(32767, 7), 229322, 8]-NRT-code), using
(49−7, 49, 119082)-Net in Base 2 — Upper bound on s
There is no (42, 49, 119083)-net in base 2, because
- 1 times m-reduction [i] would yield (42, 48, 119083)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 281 476286 921478 > 248 [i]