MinT - Best Known (55−23, 55, s)-Nets in Base 3

Best Known (55−23, 55, s)-Nets in Base 3

(55−23, 55, 60)-Net over F₃ — Constructive and digital

Digital (32, 55, 60)-net over F₃, using

1 times m-reduction [i] based on digital (32, 56, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 28, 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]

(55−23, 55, 61)-Net over F₃ — Digital

Digital (32, 55, 61)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−23, 55, 529)-Net in Base 3 — Upper bound on s

There is no (32, 55, 530)-net in base 3, because

1 times m-reduction [i] would yield (32, 54, 530)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 58 908477 866565 111886 169409 > 3⁵⁴ [i]