MinT - Best Known (67−29, 67, s)-Nets in Base 3

Best Known (67−29, 67, s)-Nets in Base 3

(67−29, 67, 60)-Net over F₃ — Constructive and digital

Digital (38, 67, 60)-net over F₃, using

1 times m-reduction [i] based on digital (38, 68, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 34, 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]

(67−29, 67, 63)-Net over F₃ — Digital

Digital (38, 67, 63)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−29, 67, 523)-Net in Base 3 — Upper bound on s

There is no (38, 67, 524)-net in base 3, because

1 times m-reduction [i] would yield (38, 66, 524)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 31 457420 397819 886725 314603 224713 > 3⁶⁶ [i]