MinT - Best Known (119−45, 119, s)-Nets in Base 3

Best Known (119−45, 119, s)-Nets in Base 3

(119−45, 119, 128)-Net over F₃ — Constructive and digital

Digital (74, 119, 128)-net over F₃, using

3 times m-reduction [i] based on digital (74, 122, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 61, 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]

(119−45, 119, 142)-Net over F₃ — Digital

Digital (74, 119, 142)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−45, 119, 1618)-Net in Base 3 — Upper bound on s

There is no (74, 119, 1619)-net in base 3, because

1 times m-reduction [i] would yield (74, 118, 1619)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199 842943 950713 955369 253564 820791 354756 111455 028808 086301 > 3¹¹⁸ [i]