MinT - Best Known (180, 180+60, s)-Nets in Base 3

Best Known (180, 180+60, s)-Nets in Base 3

(180, 180+60, 328)-Net over F₃ — Constructive and digital

Digital (180, 240, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 60, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(180, 180+60, 988)-Net over F₃ — Digital

Digital (180, 240, 988)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+60, 39482)-Net in Base 3 — Upper bound on s

There is no (180, 240, 39483)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 230516 968109 758907 541714 597004 535990 662858 635726 660108 843132 759333 144510 999434 380633 219462 132918 020364 885691 178845 > 3²⁴⁰ [i]