MinT - Best Known (187−43, 187, s)-Nets in Base 3

Best Known (187−43, 187, s)-Nets in Base 3

(187−43, 187, 464)-Net over F₃ — Constructive and digital

Digital (144, 187, 464)-net over F₃, using

t-expansion [i] based on digital (143, 187, 464)-net over F₃, using
- 1 times m-reduction [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]

(187−43, 187, 1120)-Net over F₃ — Digital

Digital (144, 187, 1120)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−43, 187, 72991)-Net in Base 3 — Upper bound on s

There is no (144, 187, 72992)-net in base 3, because

1 times m-reduction [i] would yield (144, 186, 72992)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55542 740060 133740 226957 125884 489092 946941 998715 664283 620440 535809 808384 801409 856366 906945 > 3¹⁸⁶ [i]