MinT - Best Known (189−41, 189, s)-Nets in Base 3

Best Known (189−41, 189, s)-Nets in Base 3

(189−41, 189, 640)-Net over F₃ — Constructive and digital

Digital (148, 189, 640)-net over F₃, using

3¹ times duplication [i] based on digital (147, 188, 640)-net over F₃, using
- t-expansion [i] based on digital (146, 188, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 47, 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]

(189−41, 189, 1436)-Net over F₃ — Digital

Digital (148, 189, 1436)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−41, 189, 126808)-Net in Base 3 — Upper bound on s

There is no (148, 189, 126809)-net in base 3, because

1 times m-reduction [i] would yield (148, 188, 126809)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 499818 506169 223115 049882 409711 510994 274044 695036 724085 935007 794401 713257 041175 277656 889297 > 3¹⁸⁸ [i]