MinT - Best Known (199−83, 199, s)-Nets in Base 3

Best Known (199−83, 199, s)-Nets in Base 3

(199−83, 199, 128)-Net over F₃ — Constructive and digital

Digital (116, 199, 128)-net over F₃, using

7 times m-reduction [i] based on digital (116, 206, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 103, 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]

(199−83, 199, 165)-Net over F₃ — Digital

Digital (116, 199, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−83, 199, 1585)-Net in Base 3 — Upper bound on s

There is no (116, 199, 1586)-net in base 3, because

1 times m-reduction [i] would yield (116, 198, 1586)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29831 150661 991571 998490 169889 311495 562823 444787 897184 408134 663031 233623 862201 448418 569733 318997 > 3¹⁹⁸ [i]