Best Known (39, 72, s)-Nets in Base 2
(39, 72, 33)-Net over F2 — Constructive and digital
Digital (39, 72, 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, 72, 116)-Net in Base 2 — Upper bound on s
There is no (39, 72, 117)-net in base 2, because
- 1 times m-reduction [i] would yield (39, 71, 117)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(271, 117, S2, 32), but
- the linear programming bound shows that M ≥ 436299 229870 540803 344540 378506 426337 722368 / 173 222223 038567 257555 > 271 [i]
- extracting embedded orthogonal array [i] would yield OA(271, 117, S2, 32), but