MinT - Best Known (232−72, 232, s)-Nets in Base 3

Best Known (232−72, 232, s)-Nets in Base 3

(232−72, 232, 204)-Net over F₃ — Constructive and digital

Digital (160, 232, 204)-net over F₃, using

3¹ times duplication [i] based on digital (159, 231, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 77, 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]

(232−72, 232, 454)-Net over F₃ — Digital

Digital (160, 232, 454)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−72, 232, 8446)-Net in Base 3 — Upper bound on s

There is no (160, 232, 8447)-net in base 3, because

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]