MinT - Best Known (59, 59+50, s)-Nets in Base 9

Best Known (59, 59+50, s)-Nets in Base 9

(59, 59+50, 300)-Net over F₉ — Constructive and digital

Digital (59, 109, 300)-net over F₉, using

1 times m-reduction [i] based on digital (59, 110, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 55, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(59, 59+50, 308)-Net over F₉ — Digital

Digital (59, 109, 308)-net over F₉, using

1 times m-reduction [i] based on digital (59, 110, 308)-net over F₉, using
- trace code for nets [i] based on digital (4, 55, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(59, 59+50, 18394)-Net in Base 9 — Upper bound on s

There is no (59, 109, 18395)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 103 043415 123108 985651 331399 748709 348296 837609 480514 945360 842164 387307 919102 666117 932165 452214 735169 466649 > 9¹⁰⁹ [i]