MinT - Best Known (111, 241, s)-Nets in Base 3

Best Known (111, 241, s)-Nets in Base 3

(111, 241, 74)-Net over F₃ — Constructive and digital

Digital (111, 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]

(111, 241, 104)-Net over F₃ — Digital

Digital (111, 241, 104)-net over F₃, using

t-expansion [i] based on digital (102, 241, 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]

(111, 241, 673)-Net in Base 3 — Upper bound on s

There is no (111, 241, 674)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 171710 014323 457561 060658 177281 840370 611247 374634 743100 353126 836611 045653 712673 270000 066508 473035 506748 296391 161541 > 3²⁴¹ [i]