MinT - Best Known (119−42, 119, s)-Nets in Base 3

Best Known (119−42, 119, s)-Nets in Base 3

(119−42, 119, 148)-Net over F₃ — Constructive and digital

Digital (77, 119, 148)-net over F₃, using

1 times m-reduction [i] based on digital (77, 120, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 60, 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]

(119−42, 119, 175)-Net over F₃ — Digital

Digital (77, 119, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−42, 119, 2173)-Net in Base 3 — Upper bound on s

There is no (77, 119, 2174)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 603 951386 876895 754245 965945 705210 993699 579692 183322 531829 > 3¹¹⁹ [i]