MinT - Best Known (241−125, 241, s)-Nets in Base 3

Best Known (241−125, 241, s)-Nets in Base 3

(241−125, 241, 74)-Net over F₃ — Constructive and digital

Digital (116, 241, 74)-net over F₃, using

t-expansion [i] based on digital (107, 241, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [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]

(241−125, 241, 120)-Net over F₃ — Digital

Digital (116, 241, 120)-net over F₃, using

t-expansion [i] based on digital (113, 241, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(241−125, 241, 781)-Net in Base 3 — Upper bound on s

There is no (116, 241, 782)-net in base 3, because

1 times m-reduction [i] would yield (116, 240, 782)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 355061 309184 033796 163653 854349 321654 974420 576267 426885 187062 432098 810064 975026 392107 452651 570981 733988 906659 180021 > 3²⁴⁰ [i]