MinT - Best Known (159−43, 159, s)-Nets in Base 3

Best Known (159−43, 159, s)-Nets in Base 3

(159−43, 159, 282)-Net over F₃ — Constructive and digital

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]

(159−43, 159, 523)-Net over F₃ — Digital

Digital (116, 159, 523)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−43, 159, 16854)-Net in Base 3 — Upper bound on s

There is no (116, 159, 16855)-net in base 3, because

1 times m-reduction [i] would yield (116, 158, 16855)-net in base 3, but
- 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]