MinT - Best Known (111, 111+90, s)-Nets in Base 3

Best Known (111, 111+90, s)-Nets in Base 3

(111, 111+90, 80)-Net over F₃ — Constructive and digital

Digital (111, 201, 80)-net over F₃, using

5 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+90, 137)-Net over F₃ — Digital

Digital (111, 201, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+90, 1148)-Net in Base 3 — Upper bound on s

There is no (111, 201, 1149)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 821163 370477 270598 093347 961641 702491 486715 093769 036101 172744 792810 380382 815932 105901 763782 650603 > 3²⁰¹ [i]