MinT - Best Known (187, 187+59, s)-Nets in Base 3

Best Known (187, 187+59, s)-Nets in Base 3

(187, 187+59, 464)-Net over F₃ — Constructive and digital

Digital (187, 246, 464)-net over F₃, using

3² times duplication [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]

(187, 187+59, 1191)-Net over F₃ — Digital

Digital (187, 246, 1191)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187, 187+59, 62624)-Net in Base 3 — Upper bound on s

There is no (187, 246, 62625)-net in base 3, because

1 times m-reduction [i] would yield (187, 245, 62625)-net in base 3, but
- 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]