MinT - Best Known (53−25, 53, s)-Nets in Base 9

Best Known (53−25, 53, s)-Nets in Base 9

(53−25, 53, 200)-Net over F₉ — Constructive and digital

Digital (28, 53, 200)-net over F₉, using

1 times m-reduction [i] based on digital (28, 54, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 27, 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]

(53−25, 53, 9015)-Net in Base 9 — Upper bound on s

There is no (28, 53, 9016)-net in base 9, because

1 times m-reduction [i] would yield (28, 52, 9016)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 778552 891098 995849 908887 999845 327769 797680 378625 > 9⁵² [i]