Best Known (42, 42+39, s)-Nets in Base 2
(42, 42+39, 33)-Net over F2 — Constructive and digital
Digital (42, 81, 33)-net over F2, using
- t-expansion [i] based on digital (39, 81, 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
(42, 42+39, 104)-Net in Base 2 — Upper bound on s
There is no (42, 81, 105)-net in base 2, because
- 1 times m-reduction [i] would yield (42, 80, 105)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(280, 105, S2, 38), but
- the linear programming bound shows that M ≥ 191271 407476 148169 505312 342016 / 134757 > 280 [i]
- extracting embedded orthogonal array [i] would yield OA(280, 105, S2, 38), but