Best Known (83, 83+47, s)-Nets in Base 9
(83, 83+47, 740)-Net over F9 — Constructive and digital
Digital (83, 130, 740)-net over F9, using
- 4 times m-reduction [i] based on digital (83, 134, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 67, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 67, 370)-net over F81, using
(83, 83+47, 1142)-Net over F9 — Digital
Digital (83, 130, 1142)-net over F9, using
(83, 83+47, 265093)-Net in Base 9 — Upper bound on s
There is no (83, 130, 265094)-net in base 9, because
- 1 times m-reduction [i] would yield (83, 129, 265094)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1251 110652 397559 463287 297965 363522 613368 864608 382624 026714 380674 315798 967469 834415 839189 735230 038973 965740 700754 172962 429073 > 9129 [i]