MinT - Best Known (66, 66+53, s)-Nets in Base 3

Best Known (66, 66+53, s)-Nets in Base 3

(66, 66+53, 68)-Net over F₃ — Constructive and digital

Digital (66, 119, 68)-net over F₃, using

1 times m-reduction [i] based on digital (66, 120, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 60, 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]

(66, 66+53, 89)-Net over F₃ — Digital

Digital (66, 119, 89)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+53, 746)-Net in Base 3 — Upper bound on s

There is no (66, 119, 747)-net in base 3, because

1 times m-reduction [i] would yield (66, 118, 747)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 200 201102 255961 188223 704719 900353 231824 772846 678298 080645 > 3¹¹⁸ [i]