MinT - Best Known (52, 87, s)-Nets in Base 9

Best Known (52, 87, s)-Nets in Base 9

(52, 87, 344)-Net over F₉ — Constructive and digital

Digital (52, 87, 344)-net over F₉, using

3 times m-reduction [i] based on digital (52, 90, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 45, 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]

(52, 87, 485)-Net over F₉ — Digital

Digital (52, 87, 485)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 87, 60273)-Net in Base 9 — Upper bound on s

There is no (52, 87, 60274)-net in base 9, because

1 times m-reduction [i] would yield (52, 86, 60274)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11612 120906 006125 387003 120860 694838 666231 370131 487404 742018 139815 871086 715487 890065 > 9⁸⁶ [i]