MinT - Best Known (162, 209, s)-Nets in Base 3

Best Known (162, 209, s)-Nets in Base 3

(162, 209, 640)-Net over F₃ — Constructive and digital

Digital (162, 209, 640)-net over F₃, using

3¹ times duplication [i] based on digital (161, 208, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 52, 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]

(162, 209, 1347)-Net over F₃ — Digital

Digital (162, 209, 1347)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 209, 97310)-Net in Base 3 — Upper bound on s

There is no (162, 209, 97311)-net in base 3, because

1 times m-reduction [i] would yield (162, 208, 97311)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1742 725866 968769 324435 119955 830690 097908 631518 215371 884787 651306 011538 549389 580757 365771 719827 110483 > 3²⁰⁸ [i]