MinT - Best Known (112, 112+133, s)-Nets in Base 3

Best Known (112, 112+133, s)-Nets in Base 3

(112, 112+133, 74)-Net over F₃ — Constructive and digital

Digital (112, 245, 74)-net over F₃, using

t-expansion [i] based on digital (107, 245, 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]

(112, 112+133, 104)-Net over F₃ — Digital

Digital (112, 245, 104)-net over F₃, using

t-expansion [i] based on digital (102, 245, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(112, 112+133, 674)-Net in Base 3 — Upper bound on s

There is no (112, 245, 675)-net in base 3, because

1 times m-reduction [i] would yield (112, 244, 675)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 269 917511 704035 335094 011254 240744 131896 535311 520407 605872 915057 263551 852293 144688 329319 545183 276698 481549 710936 763621 > 3²⁴⁴ [i]