MinT - Best Known (73−35, 73, s)-Nets in Base 9

Best Known (73−35, 73, s)-Nets in Base 9

(73−35, 73, 200)-Net over F₉ — Constructive and digital

Digital (38, 73, 200)-net over F₉, using

1 times m-reduction [i] based on digital (38, 74, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 37, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(73−35, 73, 9860)-Net in Base 9 — Upper bound on s

There is no (38, 73, 9861)-net in base 9, because

1 times m-reduction [i] would yield (38, 72, 9861)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 799164 238982 950039 515076 741093 361016 207453 492149 781774 450242 118825 > 9⁷² [i]