MinT - Best Known (162, 162+72, s)-Nets in Base 3

Best Known (162, 162+72, s)-Nets in Base 3

(162, 162+72, 228)-Net over F₃ — Constructive and digital

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+72, 470)-Net over F₃ — Digital

Digital (162, 234, 470)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+72, 8980)-Net in Base 3 — Upper bound on s

There is no (162, 234, 8981)-net in base 3, because

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]