MinT - Best Known (177, 177+58, s)-Nets in Base 3

Best Known (177, 177+58, s)-Nets in Base 3

(177, 177+58, 328)-Net over F₃ — Constructive and digital

Digital (177, 235, 328)-net over F₃, using

1 times m-reduction [i] based on digital (177, 236, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 59, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(177, 177+58, 1021)-Net over F₃ — Digital

Digital (177, 235, 1021)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177, 177+58, 42867)-Net in Base 3 — Upper bound on s

There is no (177, 235, 42868)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13291 152348 814041 122649 512549 449010 813090 177100 209656 355015 455344 777623 179138 209215 087751 851198 957820 524739 562569 > 3²³⁵ [i]