MinT - Best Known (21−9, 21, s)-Nets in Base 3

Best Known (21−9, 21, s)-Nets in Base 3

(21−9, 21, 32)-Net over F₃ — Constructive and digital

Digital (12, 21, 32)-net over F₃, using

1 times m-reduction [i] based on digital (12, 22, 32)-net over F₃, using
- trace code for nets [i] based on digital (1, 11, 16)-net over F₉, using
  - net from sequence [i] based on digital (1, 15)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
      - a function field by GarcÃa and Quoos [i]

(21−9, 21, 35)-Net over F₃ — Digital

Digital (12, 21, 35)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(21−9, 21, 265)-Net in Base 3 — Upper bound on s

There is no (12, 21, 266)-net in base 3, because

1 times m-reduction [i] would yield (12, 20, 266)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3515 780521 > 3²⁰ [i]