Best Known (39, 39+15, s)-Nets in Base 2
(39, 39+15, 72)-Net over F2 — Constructive and digital
Digital (39, 54, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 18, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
(39, 39+15, 82)-Net over F2 — Digital
Digital (39, 54, 82)-net over F2, using
(39, 39+15, 632)-Net in Base 2 — Upper bound on s
There is no (39, 54, 633)-net in base 2, because
- 1 times m-reduction [i] would yield (39, 53, 633)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 9010 005759 115264 > 253 [i]