MinT - Best Known (176−53, 176, s)-Nets in Base 3

Best Known (176−53, 176, s)-Nets in Base 3

(176−53, 176, 204)-Net over F₃ — Constructive and digital

Digital (123, 176, 204)-net over F₃, using

1 times m-reduction [i] based on digital (123, 177, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 59, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(176−53, 176, 392)-Net over F₃ — Digital

Digital (123, 176, 392)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−53, 176, 8557)-Net in Base 3 — Upper bound on s

There is no (123, 176, 8558)-net in base 3, because

1 times m-reduction [i] would yield (123, 175, 8558)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313612 930400 020512 064812 778097 739935 897589 141631 387062 393089 774105 611172 356005 680589 > 3¹⁷⁵ [i]