MinT - Best Known (162, 162+75, s)-Nets in Base 3

Best Known (162, 162+75, s)-Nets in Base 3

(162, 162+75, 192)-Net over F₃ — Constructive and digital

Digital (162, 237, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 79, 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]

(162, 162+75, 434)-Net over F₃ — Digital

Digital (162, 237, 434)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+75, 8057)-Net in Base 3 — Upper bound on s

There is no (162, 237, 8058)-net in base 3, because

1 times m-reduction [i] would yield (162, 236, 8058)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40019 149017 140792 168884 704017 000338 805742 596772 771507 126397 023739 788972 741195 504565 250813 451818 638947 324207 985549 > 3²³⁶ [i]