MinT - Best Known (197−77, 197, s)-Nets in Base 3

Best Known (197−77, 197, s)-Nets in Base 3

(197−77, 197, 148)-Net over F₃ — Constructive and digital

Digital (120, 197, 148)-net over F₃, using

9 times m-reduction [i] based on digital (120, 206, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 103, 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]

(197−77, 197, 197)-Net over F₃ — Digital

Digital (120, 197, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−77, 197, 2134)-Net in Base 3 — Upper bound on s

There is no (120, 197, 2135)-net in base 3, because

1 times m-reduction [i] would yield (120, 196, 2135)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3334 701978 830740 365583 223619 070550 935169 479803 851823 130177 951894 450616 527407 820564 020283 016613 > 3¹⁹⁶ [i]