MinT - Best Known (249−54, 249, s)-Nets in Base 3

Best Known (249−54, 249, s)-Nets in Base 3

(249−54, 249, 688)-Net over F₃ — Constructive and digital

Digital (195, 249, 688)-net over F₃, using

3¹ times duplication [i] based on digital (194, 248, 688)-net over F₃, using
- t-expansion [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]

(249−54, 249, 1822)-Net over F₃ — Digital

Digital (195, 249, 1822)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−54, 249, 137218)-Net in Base 3 — Upper bound on s

There is no (195, 249, 137219)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63573 479199 150401 676990 737119 861112 403280 728028 745914 054484 041414 277590 322247 565523 629116 597083 207027 596210 329749 040123 > 3²⁴⁹ [i]