Best Known (127, 127+99, s)-Nets in Base 2
(127, 127+99, 66)-Net over F2 — Constructive and digital
Digital (127, 226, 66)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 88, 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 (39, 138, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2 (see above)
- digital (39, 88, 33)-net over F2, using
(127, 127+99, 83)-Net over F2 — Digital
Digital (127, 226, 83)-net over F2, using
(127, 127+99, 392)-Net in Base 2 — Upper bound on s
There is no (127, 226, 393)-net in base 2, because
- 1 times m-reduction [i] would yield (127, 225, 393)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 55 373015 251326 860071 417653 386729 851041 441890 446874 422882 773616 413456 > 2225 [i]