MinT - Best Known (21, 21+12, s)-Nets in Base 3

Best Known (21, 21+12, s)-Nets in Base 3

(21, 21+12, 60)-Net over F₃ — Constructive and digital

Digital (21, 33, 60)-net over F₃, using

1 times m-reduction [i] based on digital (21, 34, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 17, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(21, 21+12, 69)-Net over F₃ — Digital

Digital (21, 33, 69)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(21, 21+12, 624)-Net in Base 3 — Upper bound on s

There is no (21, 33, 625)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5583 095124 659001 > 3³³ [i]