MinT - Best Known (141, 141+54, s)-Nets in Base 3

Best Known (141, 141+54, s)-Nets in Base 3

(141, 141+54, 288)-Net over F₃ — Constructive and digital

Digital (141, 195, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 65, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(141, 141+54, 568)-Net over F₃ — Digital

Digital (141, 195, 568)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+54, 15222)-Net in Base 3 — Upper bound on s

There is no (141, 195, 15223)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1093 235229 816555 461775 660427 261767 759885 637868 791904 491175 375216 098907 338016 731758 801677 725483 > 3¹⁹⁵ [i]