MinT - Best Known (189−44, 189, s)-Nets in Base 3

Best Known (189−44, 189, s)-Nets in Base 3

(189−44, 189, 464)-Net over F₃ — Constructive and digital

Digital (145, 189, 464)-net over F₃, using

3¹ times duplication [i] based on digital (144, 188, 464)-net over F₃, using
- t-expansion [i] based on digital (143, 188, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 47, 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]

(189−44, 189, 1077)-Net over F₃ — Digital

Digital (145, 189, 1077)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−44, 189, 56828)-Net in Base 3 — Upper bound on s

There is no (145, 189, 56829)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 499847 457177 719703 294303 911015 021840 884753 902596 758372 832734 030805 381999 778320 520751 810097 > 3¹⁸⁹ [i]