MinT - Best Known (163, 163+67, s)-Nets in Base 3

Best Known (163, 163+67, s)-Nets in Base 3

(163, 163+67, 264)-Net over F₃ — Constructive and digital

Digital (163, 230, 264)-net over F₃, using

1 times m-reduction [i] based on digital (163, 231, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 77, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(163, 163+67, 551)-Net over F₃ — Digital

Digital (163, 230, 551)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+67, 13434)-Net in Base 3 — Upper bound on s

There is no (163, 230, 13435)-net in base 3, because

1 times m-reduction [i] would yield (163, 229, 13435)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 270053 697492 360829 406863 181129 632535 001495 853065 079045 409688 812511 068869 363557 689523 899021 797533 730900 402615 > 3²²⁹ [i]