MinT - Best Known (167, 167+47, s)-Nets in Base 3

Best Known (167, 167+47, s)-Nets in Base 3

(167, 167+47, 640)-Net over F₃ — Constructive and digital

Digital (167, 214, 640)-net over F₃, using

2 times m-reduction [i] based on digital (167, 216, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 54, 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]

(167, 167+47, 1515)-Net over F₃ — Digital

Digital (167, 214, 1515)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+47, 123567)-Net in Base 3 — Upper bound on s

There is no (167, 214, 123568)-net in base 3, because

1 times m-reduction [i] would yield (167, 213, 123568)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423498 996575 636516 504046 958042 122674 740468 732913 717527 907133 989010 360865 223511 552691 797106 443531 716673 > 3²¹³ [i]