MinT - Best Known (197−85, 197, s)-Nets in Base 3

Best Known (197−85, 197, s)-Nets in Base 3

(197−85, 197, 128)-Net over F₃ — Constructive and digital

Digital (112, 197, 128)-net over F₃, using

1 times m-reduction [i] based on digital (112, 198, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 99, 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]

(197−85, 197, 149)-Net over F₃ — Digital

Digital (112, 197, 149)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−85, 197, 1350)-Net in Base 3 — Upper bound on s

There is no (112, 197, 1351)-net in base 3, because

1 times m-reduction [i] would yield (112, 196, 1351)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3375 391178 178385 515556 566772 658097 023621 068195 705026 693853 430293 719321 048644 751067 778987 161533 > 3¹⁹⁶ [i]