MinT - Best Known (177, 234, s)-Nets in Base 3

Best Known (177, 234, s)-Nets in Base 3

(177, 234, 400)-Net over F₃ — Constructive and digital

Digital (177, 234, 400)-net over F₃, using

3² times duplication [i] based on digital (175, 232, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 58, 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]

(177, 234, 1072)-Net over F₃ — Digital

Digital (177, 234, 1072)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 234, 52732)-Net in Base 3 — Upper bound on s

There is no (177, 234, 52733)-net in base 3, because

1 times m-reduction [i] would yield (177, 233, 52733)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1476 885915 472126 051549 742531 174729 392457 160706 424845 951754 931695 379776 803809 650634 786525 522743 253793 718663 084721 > 3²³³ [i]