MinT - Best Known (151, 151+43, s)-Nets in Base 3

Best Known (151, 151+43, s)-Nets in Base 3

(151, 151+43, 640)-Net over F₃ — Constructive and digital

Digital (151, 194, 640)-net over F₃, using

3² times duplication [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]

(151, 151+43, 1341)-Net over F₃ — Digital

Digital (151, 194, 1341)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+43, 105280)-Net in Base 3 — Upper bound on s

There is no (151, 194, 105281)-net in base 3, because

1 times m-reduction [i] would yield (151, 193, 105281)-net in base 3, but
- 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]