MinT - Best Known (116, 158, s)-Nets in Base 3

Best Known (116, 158, s)-Nets in Base 3

(116, 158, 282)-Net over F₃ — Constructive and digital

Digital (116, 158, 282)-net over F₃, using

1 times m-reduction [i] based on digital (116, 159, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 53, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(116, 158, 555)-Net over F₃ — Digital

Digital (116, 158, 555)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 158, 16854)-Net in Base 3 — Upper bound on s

There is no (116, 158, 16855)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2430 356622 823873 055929 099654 667445 332848 186249 318413 936291 568252 415902 616391 > 3¹⁵⁸ [i]