Best Known (39, 39+186, s)-Nets in Base 2
(39, 39+186, 33)-Net over F2 — Constructive and digital
Digital (39, 225, 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
(39, 39+186, 49)-Net in Base 2 — Upper bound on s
There is no (39, 225, 50)-net in base 2, because
- 34 times m-reduction [i] would yield (39, 191, 50)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2191, 50, S2, 4, 152), but
- the LP bound with quadratic polynomials shows that M ≥ 528845 821206 327854 353165 258905 245895 556623 446196 094907 711488 / 153 > 2191 [i]
- extracting embedded OOA [i] would yield OOA(2191, 50, S2, 4, 152), but