MinT - Best Known (174−41, 174, s)-Nets in Base 3

Best Known (174−41, 174, s)-Nets in Base 3

(174−41, 174, 464)-Net over F₃ — Constructive and digital

Digital (133, 174, 464)-net over F₃, using

3² times duplication [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]

(174−41, 174, 958)-Net over F₃ — Digital

Digital (133, 174, 958)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−41, 174, 55618)-Net in Base 3 — Upper bound on s

There is no (133, 174, 55619)-net in base 3, because

1 times m-reduction [i] would yield (133, 173, 55619)-net in base 3, but
- 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]