MinT - Best Known (193−42, 193, s)-Nets in Base 3

Best Known (193−42, 193, s)-Nets in Base 3

(193−42, 193, 640)-Net over F₃ — Constructive and digital

Digital (151, 193, 640)-net over F₃, using

3¹ times duplication [i] based on digital (150, 192, 640)-net over F₃, using
- t-expansion [i] based on digital (149, 192, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 48, 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]

(193−42, 193, 1442)-Net over F₃ — Digital

Digital (151, 193, 1442)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−42, 193, 105280)-Net in Base 3 — Upper bound on s

There is no (151, 193, 105281)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 453927 651081 620362 783566 650725 310355 331809 765878 229588 568338 668979 680031 302977 863876 634931 > 3¹⁹³ [i]