Best Known (202−162, 202, s)-Nets in Base 2
(202−162, 202, 33)-Net over F2 — Constructive and digital
Digital (40, 202, 33)-net over F2, using
- t-expansion [i] based on digital (39, 202, 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
(202−162, 202, 50)-Net in Base 2 — Upper bound on s
There is no (40, 202, 51)-net in base 2, because
- 7 times m-reduction [i] would yield (40, 195, 51)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2195, 51, S2, 4, 155), but
- the LP bound with quadratic polynomials shows that M ≥ 2 021226 758794 511205 955124 194272 868585 984958 453117 419113 152512 / 39 > 2195 [i]
- extracting embedded OOA [i] would yield OOA(2195, 51, S2, 4, 155), but