Best Known (37, 72, s)-Nets in Base 8
(37, 72, 160)-Net over F8 — Constructive and digital
Digital (37, 72, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 36, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(37, 72, 162)-Net over F8 — Digital
Digital (37, 72, 162)-net over F8, using
- trace code for nets [i] based on digital (1, 36, 81)-net over F64, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
(37, 72, 6051)-Net in Base 8 — Upper bound on s
There is no (37, 72, 6052)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 71, 6052)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 13200 308737 069507 735885 334515 836436 281620 828265 611152 290705 438982 > 871 [i]