MinT - Best Known (41−15, 41, s)-Nets in Base 3

Best Known (41−15, 41, s)-Nets in Base 3

(41−15, 41, 64)-Net over F₃ — Constructive and digital

Digital (26, 41, 64)-net over F₃, using

1 times m-reduction [i] based on digital (26, 42, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 21, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]

(41−15, 41, 74)-Net over F₃ — Digital

Digital (26, 41, 74)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(41−15, 41, 893)-Net in Base 3 — Upper bound on s

There is no (26, 41, 894)-net in base 3, because

1 times m-reduction [i] would yield (26, 40, 894)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12 192678 542893 318713 > 3⁴⁰ [i]