Best Known (44, 79, s)-Nets in Base 9
(44, 79, 300)-Net over F9 — Constructive and digital
Digital (44, 79, 300)-net over F9, using
- 1 times m-reduction [i] based on digital (44, 80, 300)-net over F9, using
- trace code for nets [i] based on digital (4, 40, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 40, 150)-net over F81, using
(44, 79, 308)-Net over F9 — Digital
Digital (44, 79, 308)-net over F9, using
- 1 times m-reduction [i] based on digital (44, 80, 308)-net over F9, using
- trace code for nets [i] based on digital (4, 40, 154)-net over F81, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- trace code for nets [i] based on digital (4, 40, 154)-net over F81, using
(44, 79, 21425)-Net in Base 9 — Upper bound on s
There is no (44, 79, 21426)-net in base 9, because
- 1 times m-reduction [i] would yield (44, 78, 21426)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 269 741357 314613 154101 400884 512073 493374 620555 074122 243778 772468 443455 704209 > 978 [i]