MinT - Best Known (51−23, 51, s)-Nets in Base 3

Best Known (51−23, 51, s)-Nets in Base 3

(51−23, 51, 40)-Net over F₃ — Constructive and digital

Digital (28, 51, 40)-net over F₃, using

1 times m-reduction [i] based on digital (28, 52, 40)-net over F₃, using
- trace code for nets [i] based on digital (2, 26, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]

(51−23, 51, 46)-Net over F₃ — Digital

Digital (28, 51, 46)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−23, 51, 351)-Net in Base 3 — Upper bound on s

There is no (28, 51, 352)-net in base 3, because

1 times m-reduction [i] would yield (28, 50, 352)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 725946 004106 244853 898625 > 3⁵⁰ [i]