MinT - Best Known (47−17, 47, s)-Nets in Base 3

Best Known (47−17, 47, s)-Nets in Base 3

(47−17, 47, 68)-Net over F₃ — Constructive and digital

Digital (30, 47, 68)-net over F₃, using

1 times m-reduction [i] based on digital (30, 48, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 24, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(47−17, 47, 83)-Net over F₃ — Digital

Digital (30, 47, 83)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(47−17, 47, 1035)-Net in Base 3 — Upper bound on s

There is no (30, 47, 1036)-net in base 3, because

1 times m-reduction [i] would yield (30, 46, 1036)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8924 500972 454754 765249 > 3⁴⁶ [i]