MinT - Best Known (162, 162+71, s)-Nets in Base 3

Best Known (162, 162+71, s)-Nets in Base 3

(162, 162+71, 228)-Net over F₃ — Constructive and digital

Digital (162, 233, 228)-net over F₃, using

1 times m-reduction [i] based on digital (162, 234, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 78, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(162, 162+71, 482)-Net over F₃ — Digital

Digital (162, 233, 482)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+71, 10078)-Net in Base 3 — Upper bound on s

There is no (162, 233, 10079)-net in base 3, because

1 times m-reduction [i] would yield (162, 232, 10079)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 493 509144 723004 800951 424564 489454 358230 081961 934571 826019 542207 009495 445150 783930 667644 619014 459221 019911 707451 > 3²³² [i]