MinT - Best Known (57, 57+35, s)-Nets in Base 9

Best Known (57, 57+35, s)-Nets in Base 9

(57, 57+35, 344)-Net over F₉ — Constructive and digital

Digital (57, 92, 344)-net over F₉, using

8 times m-reduction [i] based on digital (57, 100, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 50, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(57, 57+35, 663)-Net over F₉ — Digital

Digital (57, 92, 663)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+35, 115032)-Net in Base 9 — Upper bound on s

There is no (57, 92, 115033)-net in base 9, because

1 times m-reduction [i] would yield (57, 91, 115033)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 634465 646867 825626 312154 027956 619357 150470 082156 650141 585123 631767 015526 017062 728009 > 9⁹¹ [i]