MinT - Best Known (233−73, 233, s)-Nets in Base 3

Best Known (233−73, 233, s)-Nets in Base 3

(233−73, 233, 192)-Net over F₃ — Constructive and digital

Digital (160, 233, 192)-net over F₃, using

1 times m-reduction [i] based on digital (160, 234, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 78, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(233−73, 233, 442)-Net over F₃ — Digital

Digital (160, 233, 442)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−73, 233, 8446)-Net in Base 3 — Upper bound on s

There is no (160, 233, 8447)-net in base 3, because

1 times m-reduction [i] would yield (160, 232, 8447)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 493 503039 933602 309097 453859 027812 393701 301027 597498 846282 968231 516885 066646 148571 481884 764149 474919 404177 514425 > 3²³² [i]