MinT - Best Known (189, 189+61, s)-Nets in Base 3

Best Known (189, 189+61, s)-Nets in Base 3

(189, 189+61, 400)-Net over F₃ — Constructive and digital

Digital (189, 250, 400)-net over F₃, using

3² times duplication [i] based on digital (187, 248, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 62, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(189, 189+61, 1126)-Net over F₃ — Digital

Digital (189, 250, 1126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189, 189+61, 54907)-Net in Base 3 — Upper bound on s

There is no (189, 250, 54908)-net in base 3, because

1 times m-reduction [i] would yield (189, 249, 54908)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63577 727111 084970 765176 081676 438984 507651 011718 698767 591949 541613 135529 465725 207337 690068 706133 858016 183333 044898 479145 > 3²⁴⁹ [i]