MinT - Best Known (55, 55+45, s)-Nets in Base 3

Best Known (55, 55+45, s)-Nets in Base 3

(55, 55+45, 64)-Net over F₃ — Constructive and digital

Digital (55, 100, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 50, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(55, 55+45, 76)-Net over F₃ — Digital

Digital (55, 100, 76)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+45, 613)-Net in Base 3 — Upper bound on s

There is no (55, 100, 614)-net in base 3, because

1 times m-reduction [i] would yield (55, 99, 614)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 172163 422177 357067 986284 828435 701194 552398 799413 > 3⁹⁹ [i]