MinT - Best Known (173−40, 173, s)-Nets in Base 3

Best Known (173−40, 173, s)-Nets in Base 3

(173−40, 173, 464)-Net over F₃ — Constructive and digital

Digital (133, 173, 464)-net over F₃, using

3¹ times duplication [i] based on digital (132, 172, 464)-net over F₃, using
- t-expansion [i] based on digital (131, 172, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 43, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(173−40, 173, 1026)-Net over F₃ — Digital

Digital (133, 173, 1026)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−40, 173, 55618)-Net in Base 3 — Upper bound on s

There is no (133, 173, 55619)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34832 376835 857172 117040 247518 570869 540741 913279 285952 135772 605708 646467 946930 613433 > 3¹⁷³ [i]