MinT - Best Known (92−33, 92, s)-Nets in Base 9

Best Known (92−33, 92, s)-Nets in Base 9

(92−33, 92, 448)-Net over F₉ — Constructive and digital

Digital (59, 92, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 46, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(92−33, 92, 902)-Net over F₉ — Digital

Digital (59, 92, 902)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−33, 92, 227344)-Net in Base 9 — Upper bound on s

There is no (59, 92, 227345)-net in base 9, because

1 times m-reduction [i] would yield (59, 91, 227345)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 609880 075989 381106 224517 363598 710897 314726 613176 640051 899450 479854 244206 412473 046657 > 9⁹¹ [i]