Best Known (134, 134+83, s)-Nets in Base 2
(134, 134+83, 75)-Net over F2 — Constructive and digital
Digital (134, 217, 75)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 80, 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, 137, 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, 80, 33)-net over F2, using
(134, 134+83, 109)-Net over F2 — Digital
Digital (134, 217, 109)-net over F2, using
(134, 134+83, 563)-Net in Base 2 — Upper bound on s
There is no (134, 217, 564)-net in base 2, because
- 1 times m-reduction [i] would yield (134, 216, 564)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 107771 908920 831897 464615 456961 811744 417983 278755 429795 247315 970450 > 2216 [i]