MinT - Best Known (111, 111+92, s)-Nets in Base 3

Best Known (111, 111+92, s)-Nets in Base 3

(111, 111+92, 80)-Net over F₃ — Constructive and digital

Digital (111, 203, 80)-net over F₃, using

3 times m-reduction [i] based on digital (111, 206, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 103, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(111, 111+92, 133)-Net over F₃ — Digital

Digital (111, 203, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+92, 1102)-Net in Base 3 — Upper bound on s

There is no (111, 203, 1103)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 244720 844036 898901 147948 797866 097766 411701 863373 251029 444488 846055 052060 064404 255673 923292 033477 > 3²⁰³ [i]