MinT - Best Known (53, 53+35, s)-Nets in Base 9

Best Known (53, 53+35, s)-Nets in Base 9

(53, 53+35, 344)-Net over F₉ — Constructive and digital

Digital (53, 88, 344)-net over F₉, using

4 times m-reduction [i] based on digital (53, 92, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 46, 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]

(53, 53+35, 516)-Net over F₉ — Digital

Digital (53, 88, 516)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+35, 68591)-Net in Base 9 — Upper bound on s

There is no (53, 88, 68592)-net in base 9, because

1 times m-reduction [i] would yield (53, 87, 68592)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104520 115108 604098 588326 458630 679674 547929 277332 996686 071762 248555 357528 818088 691585 > 9⁸⁷ [i]