MinT - Best Known (247−54, 247, s)-Nets in Base 3

Best Known (247−54, 247, s)-Nets in Base 3

(247−54, 247, 688)-Net over F₃ — Constructive and digital

Digital (193, 247, 688)-net over F₃, using

1 times m-reduction [i] based on digital (193, 248, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 62, 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]

(247−54, 247, 1749)-Net over F₃ — Digital

Digital (193, 247, 1749)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−54, 247, 126491)-Net in Base 3 — Upper bound on s

There is no (193, 247, 126492)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7062 944648 697167 783266 050744 871936 864336 290256 619962 226916 915880 679210 581577 411053 724004 928036 572798 307602 516476 005841 > 3²⁴⁷ [i]