MinT - Best Known (67, 112, s)-Nets in Base 3

Best Known (67, 112, s)-Nets in Base 3

(67, 112, 80)-Net over F₃ — Constructive and digital

Digital (67, 112, 80)-net over F₃, using

6 times m-reduction [i] based on digital (67, 118, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 59, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(67, 112, 114)-Net over F₃ — Digital

Digital (67, 112, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 112, 1135)-Net in Base 3 — Upper bound on s

There is no (67, 112, 1136)-net in base 3, because

1 times m-reduction [i] would yield (67, 111, 1136)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 92894 499237 745927 264924 922788 809203 751567 733103 603361 > 3¹¹¹ [i]