Best Known (39, 243, s)-Nets in Base 2
(39, 243, 33)-Net over F2 — Constructive and digital
Digital (39, 243, 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, 243, 48)-Net in Base 2 — Upper bound on s
There is no (39, 243, 49)-net in base 2, because
- 8 times m-reduction [i] would yield (39, 235, 49)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2235, 49, S2, 5, 196), but
- the LP bound with quadratic polynomials shows that M ≥ 64 489917 864411 028029 790358 777116 525827 703162 235960 091971 438626 347180 621824 / 985 > 2235 [i]
- extracting embedded OOA [i] would yield OOA(2235, 49, S2, 5, 196), but