MinT - Best Known (79−35, 79, s)-Nets in Base 3

Best Known (79−35, 79, s)-Nets in Base 3

(79−35, 79, 60)-Net over F₃ — Constructive and digital

Digital (44, 79, 60)-net over F₃, using

1 times m-reduction [i] based on digital (44, 80, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 40, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(79−35, 79, 66)-Net over F₃ — Digital

Digital (44, 79, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−35, 79, 538)-Net in Base 3 — Upper bound on s

There is no (44, 79, 539)-net in base 3, because

1 times m-reduction [i] would yield (44, 78, 539)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 725698 863429 363451 217787 952822 406807 > 3⁷⁸ [i]