MinT - Best Known (70, 70+59, s)-Nets in Base 3

Best Known (70, 70+59, s)-Nets in Base 3

(70, 70+59, 64)-Net over F₃ — Constructive and digital

Digital (70, 129, 64)-net over F₃, using

1 times m-reduction [i] based on digital (70, 130, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 65, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+59, 89)-Net over F₃ — Digital

Digital (70, 129, 89)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+59, 716)-Net in Base 3 — Upper bound on s

There is no (70, 129, 717)-net in base 3, because

1 times m-reduction [i] would yield (70, 128, 717)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 933650 704935 139954 871733 553303 637083 072316 113866 925303 899083 > 3¹²⁸ [i]