MinT - Best Known (53−21, 53, s)-Nets in Base 3

Best Known (53−21, 53, s)-Nets in Base 3

(53−21, 53, 64)-Net over F₃ — Constructive and digital

Digital (32, 53, 64)-net over F₃, using

1 times m-reduction [i] based on digital (32, 54, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 27, 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]

(53−21, 53, 69)-Net over F₃ — Digital

Digital (32, 53, 69)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−21, 53, 676)-Net in Base 3 — Upper bound on s

There is no (32, 53, 677)-net in base 3, because

1 times m-reduction [i] would yield (32, 52, 677)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 555346 651966 731471 042609 > 3⁵² [i]