MinT - Best Known (112, 208, s)-Nets in Base 3

Best Known (112, 208, s)-Nets in Base 3

(112, 208, 80)-Net over F₃ — Constructive and digital

Digital (112, 208, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 104, 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]

(112, 208, 130)-Net over F₃ — Digital

Digital (112, 208, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 208, 1048)-Net in Base 3 — Upper bound on s

There is no (112, 208, 1049)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1819 654506 707218 835687 839727 082414 024972 452517 669652 419882 847969 872341 803467 636600 807685 261837 234625 > 3²⁰⁸ [i]