MinT - Best Known (137−58, 137, s)-Nets in Base 9

Best Known (137−58, 137, s)-Nets in Base 9

(137−58, 137, 344)-Net over F₉ — Constructive and digital

Digital (79, 137, 344)-net over F₉, using

7 times m-reduction [i] based on digital (79, 144, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 72, 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]

(137−58, 137, 536)-Net over F₉ — Digital

Digital (79, 137, 536)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−58, 137, 46972)-Net in Base 9 — Upper bound on s

There is no (79, 137, 46973)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53876 043901 871167 244414 813127 863356 987592 138902 578061 907205 457705 477350 742086 912661 466231 249294 356588 096644 113757 993809 451331 276233 > 9¹³⁷ [i]