Best Known (146, 146+101, s)-Nets in Base 2
(146, 146+101, 75)-Net over F2 — Constructive and digital
Digital (146, 247, 75)-net over F2, using
- 5 times m-reduction [i] based on digital (146, 252, 75)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 92, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (54, 160, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (39, 92, 33)-net over F2, using
- (u, u+v)-construction [i] based on
(146, 146+101, 105)-Net over F2 — Digital
Digital (146, 247, 105)-net over F2, using
(146, 146+101, 519)-Net in Base 2 — Upper bound on s
There is no (146, 247, 520)-net in base 2, because
- 1 times m-reduction [i] would yield (146, 246, 520)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 119 384845 875666 188233 656246 575782 058253 531835 540848 439054 118019 522264 894624 > 2246 [i]