MinT - Best Known (217−98, 217, s)-Nets in Base 3

Best Known (217−98, 217, s)-Nets in Base 3

(217−98, 217, 80)-Net over F₃ — Constructive and digital

Digital (119, 217, 80)-net over F₃, using

5 times m-reduction [i] based on digital (119, 222, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 111, 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]

(217−98, 217, 143)-Net over F₃ — Digital

Digital (119, 217, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−98, 217, 1191)-Net in Base 3 — Upper bound on s

There is no (119, 217, 1192)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 618718 485855 898851 331529 375302 132697 144150 058208 548284 501187 483156 906869 806888 273504 269059 490986 264657 > 3²¹⁷ [i]