MinT - Best Known (53, 92, s)-Nets in Base 9

Best Known (53, 92, s)-Nets in Base 9

(53, 92, 344)-Net over F₉ — Constructive and digital

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, 92, 389)-Net over F₉ — Digital

Digital (53, 92, 389)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 92, 36839)-Net in Base 9 — Upper bound on s

There is no (53, 92, 36840)-net in base 9, because

1 times m-reduction [i] would yield (53, 91, 36840)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 859463 962498 664233 046471 781204 535198 488585 191564 277694 057372 594373 082313 777773 525185 > 9⁹¹ [i]