MinT - Best Known (245−58, 245, s)-Nets in Base 3

Best Known (245−58, 245, s)-Nets in Base 3

(245−58, 245, 464)-Net over F₃ — Constructive and digital

Digital (187, 245, 464)-net over F₃, using

3¹ times duplication [i] based on digital (186, 244, 464)-net over F₃, using
- t-expansion [i] based on digital (185, 244, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 61, 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]

(245−58, 245, 1252)-Net over F₃ — Digital

Digital (187, 245, 1252)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−58, 245, 62624)-Net in Base 3 — Upper bound on s

There is no (187, 245, 62625)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 774233 800258 730623 839762 826964 743305 356083 667834 697783 302101 915798 750545 338941 062706 940038 257131 925204 264531 635411 > 3²⁴⁵ [i]