Best Known (185−142, 185, s)-Nets in Base 2
(185−142, 185, 33)-Net over F2 — Constructive and digital
Digital (43, 185, 33)-net over F2, using
- t-expansion [i] based on digital (39, 185, 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
(185−142, 185, 34)-Net over F2 — Digital
Digital (43, 185, 34)-net over F2, using
- net from sequence [i] based on digital (43, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 43 and N(F) ≥ 34, using
(185−142, 185, 57)-Net in Base 2 — Upper bound on s
There is no (43, 185, 58)-net in base 2, because
- 20 times m-reduction [i] would yield (43, 165, 58)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2165, 58, S2, 3, 122), but
- the LP bound with quadratic polynomials shows that M ≥ 7108 743963 977511 794142 723026 332000 607606 455889 035264 / 123 > 2165 [i]
- extracting embedded OOA [i] would yield OOA(2165, 58, S2, 3, 122), but