MinT - Best Known (52, 96, s)-Nets in Base 3

Best Known (52, 96, s)-Nets in Base 3

(52, 96, 60)-Net over F₃ — Constructive and digital

Digital (52, 96, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 48, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]

(52, 96, 70)-Net over F₃ — Digital

Digital (52, 96, 70)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 96, 525)-Net in Base 3 — Upper bound on s

There is no (52, 96, 526)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6461 069547 491735 822012 174608 149724 668484 299429 > 3⁹⁶ [i]