MinT - Best Known (28, 47, s)-Nets in Base 3

Best Known (28, 47, s)-Nets in Base 3

(28, 47, 60)-Net over F₃ — Constructive and digital

Digital (28, 47, 60)-net over F₃, using

1 times m-reduction [i] based on digital (28, 48, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 24, 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]

(28, 47, 560)-Net in Base 3 — Upper bound on s

There is no (28, 47, 561)-net in base 3, because

1 times m-reduction [i] would yield (28, 46, 561)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8883 569564 088463 749187 > 3⁴⁶ [i]