Best Known (142−45, 142, s)-Nets in Base 2
(142−45, 142, 69)-Net over F2 — Constructive and digital
Digital (97, 142, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 3)-net over F2, using
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 0 and N(F) ≥ 3, using
- the rational function field F2(x) [i]
- Niederreiter sequence [i]
- Sobol sequence [i]
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- digital (75, 120, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 60, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 60, 33)-net over F4, using
- digital (0, 22, 3)-net over F2, using
(142−45, 142, 72)-Net in Base 2 — Constructive
(97, 142, 72)-net in base 2, using
- trace code for nets [i] based on (26, 71, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
(142−45, 142, 119)-Net over F2 — Digital
Digital (97, 142, 119)-net over F2, using
(142−45, 142, 737)-Net in Base 2 — Upper bound on s
There is no (97, 142, 738)-net in base 2, because
- 1 times m-reduction [i] would yield (97, 141, 738)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 822596 369533 609273 327974 776874 824250 278192 > 2141 [i]