MinT - Best Known (40, 40+25, s)-Nets in Base 3

Best Known (40, 40+25, s)-Nets in Base 3

(40, 40+25, 72)-Net over F₃ — Constructive and digital

Digital (40, 65, 72)-net over F₃, using

1 times m-reduction [i] based on digital (40, 66, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 33, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(40, 40+25, 86)-Net over F₃ — Digital

Digital (40, 65, 86)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+25, 915)-Net in Base 3 — Upper bound on s

There is no (40, 65, 916)-net in base 3, because

1 times m-reduction [i] would yield (40, 64, 916)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 463029 018889 427882 910844 424833 > 3⁶⁴ [i]