MinT - Best Known (77−25, 77, s)-Nets in Base 3

Best Known (77−25, 77, s)-Nets in Base 3

(77−25, 77, 128)-Net over F₃ — Constructive and digital

Digital (52, 77, 128)-net over F₃, using

1 times m-reduction [i] based on digital (52, 78, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 39, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(77−25, 77, 161)-Net over F₃ — Digital

Digital (52, 77, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−25, 77, 2768)-Net in Base 3 — Upper bound on s

There is no (52, 77, 2769)-net in base 3, because

1 times m-reduction [i] would yield (52, 76, 2769)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 825830 561024 995207 344987 260515 933809 > 3⁷⁶ [i]