MinT - Best Known (139−63, 139, s)-Nets in Base 3

Best Known (139−63, 139, s)-Nets in Base 3

(139−63, 139, 68)-Net over F₃ — Constructive and digital

Digital (76, 139, 68)-net over F₃, using

1 times m-reduction [i] based on digital (76, 140, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 70, 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]

(139−63, 139, 97)-Net over F₃ — Digital

Digital (76, 139, 97)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−63, 139, 795)-Net in Base 3 — Upper bound on s

There is no (76, 139, 796)-net in base 3, because

1 times m-reduction [i] would yield (76, 138, 796)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 698110 137042 942621 578498 555666 200630 140683 958790 120668 948347 217105 > 3¹³⁸ [i]