MinT - Best Known (159, 235, s)-Nets in Base 3

Best Known (159, 235, s)-Nets in Base 3

(159, 235, 168)-Net over F₃ — Constructive and digital

Digital (159, 235, 168)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (11, 49, 20)-net over F₃, using
  - net from sequence [i] based on digital (11, 19)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 9, N(F)Â =Â 19, and 1 place with degree 3 [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
2. digital (110, 186, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 93, 74)-net over F₉, using
    - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]

(159, 235, 402)-Net over F₃ — Digital

Digital (159, 235, 402)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 235, 6667)-Net in Base 3 — Upper bound on s

There is no (159, 235, 6668)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13328 731028 347111 129977 286134 728062 743868 304996 716395 624425 876699 781045 430460 625554 575465 471735 079692 036874 090505 > 3²³⁵ [i]