MinT - Best Known (211−89, 211, s)-Nets in Base 3

Best Known (211−89, 211, s)-Nets in Base 3

(211−89, 211, 128)-Net over F₃ — Constructive and digital

Digital (122, 211, 128)-net over F₃, using

7 times m-reduction [i] based on digital (122, 218, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 109, 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]

(211−89, 211, 169)-Net over F₃ — Digital

Digital (122, 211, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−89, 211, 1590)-Net in Base 3 — Upper bound on s

There is no (122, 211, 1591)-net in base 3, because

1 times m-reduction [i] would yield (122, 210, 1591)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15998 820725 209402 238616 736192 587074 383020 697542 844033 035157 319402 974325 015138 266896 515043 293593 377705 > 3²¹⁰ [i]