MinT - Best Known (239−124, 239, s)-Nets in Base 3

Best Known (239−124, 239, s)-Nets in Base 3

(239−124, 239, 74)-Net over F₃ — Constructive and digital

Digital (115, 239, 74)-net over F₃, using

t-expansion [i] based on digital (107, 239, 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]

(239−124, 239, 120)-Net over F₃ — Digital

Digital (115, 239, 120)-net over F₃, using

t-expansion [i] based on digital (113, 239, 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]

(239−124, 239, 766)-Net in Base 3 — Upper bound on s

There is no (115, 239, 767)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 097725 185782 241303 409153 761191 171357 396498 846036 721813 208778 978616 467288 991982 045277 139896 432631 119038 237890 817413 > 3²³⁹ [i]