MinT - Best Known (24, 45, s)-Nets in Base 9

Best Known (24, 45, s)-Nets in Base 9

(24, 45, 200)-Net over F₉ — Constructive and digital

Digital (24, 45, 200)-net over F₉, using

1 times m-reduction [i] based on digital (24, 46, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 23, 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]

(24, 45, 8938)-Net in Base 9 — Upper bound on s

There is no (24, 45, 8939)-net in base 9, because

1 times m-reduction [i] would yield (24, 44, 8939)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 970104 095341 572883 198665 878413 145964 315633 > 9⁴⁴ [i]