MinT - Best Known (199−81, 199, s)-Nets in Base 3

Best Known (199−81, 199, s)-Nets in Base 3

(199−81, 199, 148)-Net over F₃ — Constructive and digital

Digital (118, 199, 148)-net over F₃, using

3 times m-reduction [i] based on digital (118, 202, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 101, 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]

(199−81, 199, 177)-Net over F₃ — Digital

Digital (118, 199, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−81, 199, 1774)-Net in Base 3 — Upper bound on s

There is no (118, 199, 1775)-net in base 3, because

1 times m-reduction [i] would yield (118, 198, 1775)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29952 749078 321841 531527 332977 046229 203547 646783 284988 528695 023867 199669 516062 970756 698723 770033 > 3¹⁹⁸ [i]