MinT - Best Known (96−29, 96, s)-Nets in Base 3

Best Known (96−29, 96, s)-Nets in Base 3

(96−29, 96, 156)-Net over F₃ — Constructive and digital

Digital (67, 96, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 32, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(96−29, 96, 240)-Net over F₃ — Digital

Digital (67, 96, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−29, 96, 5210)-Net in Base 3 — Upper bound on s

There is no (67, 96, 5211)-net in base 3, because

1 times m-reduction [i] would yield (67, 95, 5211)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2121 391707 391587 284110 458139 472354 159964 205117 > 3⁹⁵ [i]