MinT - Best Known (112, 200, s)-Nets in Base 3

Best Known (112, 200, s)-Nets in Base 3

(112, 200, 80)-Net over F₃ — Constructive and digital

Digital (112, 200, 80)-net over F₃, using

8 times m-reduction [i] based on 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, 200, 143)-Net over F₃ — Digital

Digital (112, 200, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 200, 1229)-Net in Base 3 — Upper bound on s

There is no (112, 200, 1230)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270107 041064 584665 367724 884597 773040 413266 348102 557970 789391 594942 851599 323713 613306 756116 736537 > 3²⁰⁰ [i]