MinT - Best Known (27, 27+23, s)-Nets in Base 3

Best Known (27, 27+23, s)-Nets in Base 3

(27, 27+23, 40)-Net over F₃ — Constructive and digital

Digital (27, 50, 40)-net over F₃, using

trace code for nets [i] based on digital (2, 25, 20)-net over F₉, using
- net from sequence [i] based on digital (2, 19)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
    - a function field by GarcÃa and Quoos [i]

(27, 27+23, 43)-Net over F₃ — Digital

Digital (27, 50, 43)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 27+23, 317)-Net in Base 3 — Upper bound on s

There is no (27, 50, 318)-net in base 3, because

1 times m-reduction [i] would yield (27, 49, 318)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 245497 506691 803151 459249 > 3⁴⁹ [i]