MinT - Best Known (177, 177+56, s)-Nets in Base 3

Best Known (177, 177+56, s)-Nets in Base 3

(177, 177+56, 464)-Net over F₃ — Constructive and digital

Digital (177, 233, 464)-net over F₃, using

3¹ times duplication [i] based on digital (176, 232, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 58, 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]

(177, 177+56, 1128)-Net over F₃ — Digital

Digital (177, 233, 1128)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+56, 52732)-Net in Base 3 — Upper bound on s

There is no (177, 233, 52733)-net in base 3, because

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]