MinT - Best Known (77−37, 77, s)-Nets in Base 9

Best Known (77−37, 77, s)-Nets in Base 9

(77−37, 77, 200)-Net over F₉ — Constructive and digital

Digital (40, 77, 200)-net over F₉, using

1 times m-reduction [i] based on digital (40, 78, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 39, 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]

(77−37, 77, 10083)-Net in Base 9 — Upper bound on s

There is no (40, 77, 10084)-net in base 9, because

1 times m-reduction [i] would yield (40, 76, 10084)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 334235 621481 142530 955737 477930 659379 372666 400772 286063 187342 628904 555201 > 9⁷⁶ [i]