MinT - Best Known (162, 162+73, s)-Nets in Base 3

Best Known (162, 162+73, s)-Nets in Base 3

(162, 162+73, 204)-Net over F₃ — Constructive and digital

Digital (162, 235, 204)-net over F₃, using

3¹ times duplication [i] based on digital (161, 234, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 78, 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]

(162, 162+73, 458)-Net over F₃ — Digital

Digital (162, 235, 458)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+73, 8980)-Net in Base 3 — Upper bound on s

There is no (162, 235, 8981)-net in base 3, because

1 times m-reduction [i] would yield (162, 234, 8981)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4444 380249 422022 996523 113242 364848 621896 826490 221462 608025 751982 213841 422455 176089 912052 172871 645534 885323 084113 > 3²³⁴ [i]