Best Known (142−35, 142, s)-Nets in Base 2
(142−35, 142, 144)-Net over F2 — Constructive and digital
Digital (107, 142, 144)-net over F2, using
- 2 times m-reduction [i] based on digital (107, 144, 144)-net over F2, using
- trace code for nets [i] based on digital (11, 48, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- trace code for nets [i] based on digital (11, 48, 48)-net over F8, using
(142−35, 142, 220)-Net over F2 — Digital
Digital (107, 142, 220)-net over F2, using
(142−35, 142, 2227)-Net in Base 2 — Upper bound on s
There is no (107, 142, 2228)-net in base 2, because
- 1 times m-reduction [i] would yield (107, 141, 2228)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 789081 732879 954674 184269 187683 114735 300779 > 2141 [i]