Best Known (37, 37+14, s)-Nets in Base 2
(37, 37+14, 72)-Net over F2 — Constructive and digital
Digital (37, 51, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 17, 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
(37, 37+14, 82)-Net over F2 — Digital
Digital (37, 51, 82)-net over F2, using
(37, 37+14, 517)-Net in Base 2 — Upper bound on s
There is no (37, 51, 518)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2267 416380 868140 > 251 [i]