MinT - Best Known (177−69, 177, s)-Nets in Base 3

Best Known (177−69, 177, s)-Nets in Base 3

(177−69, 177, 148)-Net over F₃ — Constructive and digital

Digital (108, 177, 148)-net over F₃, using

5 times m-reduction [i] based on digital (108, 182, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 91, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(177−69, 177, 181)-Net over F₃ — Digital

Digital (108, 177, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−69, 177, 1963)-Net in Base 3 — Upper bound on s

There is no (108, 177, 1964)-net in base 3, because

1 times m-reduction [i] would yield (108, 176, 1964)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 954304 375954 976814 547629 320311 741311 348332 380925 069114 209637 538504 023141 180052 060969 > 3¹⁷⁶ [i]