MinT - Best Known (241−54, 241, s)-Nets in Base 3

Best Known (241−54, 241, s)-Nets in Base 3

(241−54, 241, 640)-Net over F₃ — Constructive and digital

Digital (187, 241, 640)-net over F₃, using

3¹ times duplication [i] based on digital (186, 240, 640)-net over F₃, using
- t-expansion [i] based on digital (185, 240, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 60, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(241−54, 241, 1548)-Net over F₃ — Digital

Digital (187, 241, 1548)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−54, 241, 99085)-Net in Base 3 — Upper bound on s

There is no (187, 241, 99086)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 689343 997123 441397 050913 677150 683731 319738 295877 190746 317113 614452 752946 050520 945495 034952 836009 275997 925204 823761 > 3²⁴¹ [i]