Best Known (41, 41+6, s)-Nets in Base 2
(41, 41+6, 32766)-Net over F2 — Constructive and digital
Digital (41, 47, 32766)-net over F2, using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 6, 6) (dual of [(32766, 6), 196549, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(247, 32767, F2, 3, 6) (dual of [(32767, 3), 98254, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(247, 32767, F2, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(247, 32767, F2, 3, 6) (dual of [(32767, 3), 98254, 7]-NRT-code), using
(41, 41+6, 32767)-Net over F2 — Digital
Digital (41, 47, 32767)-net over F2, using
- t-expansion [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
(41, 41+6, 94515)-Net in Base 2 — Upper bound on s
There is no (41, 47, 94516)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 140 740758 602023 > 247 [i]