MinT - Best Known (116, 116+85, s)-Nets in Base 3

Best Known (116, 116+85, s)-Nets in Base 3

(116, 116+85, 128)-Net over F₃ — Constructive and digital

Digital (116, 201, 128)-net over F₃, using

5 times m-reduction [i] based on digital (116, 206, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 103, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(116, 116+85, 161)-Net over F₃ — Digital

Digital (116, 201, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+85, 1503)-Net in Base 3 — Upper bound on s

There is no (116, 201, 1504)-net in base 3, because

1 times m-reduction [i] would yield (116, 200, 1504)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 269816 349070 253274 557871 650650 276929 493247 043971 847371 826419 141813 427404 611662 511251 281194 715457 > 3²⁰⁰ [i]