MinT - Best Known (23, 23+13, s)-Nets in Base 3

Best Known (23, 23+13, s)-Nets in Base 3

(23, 23+13, 64)-Net over F₃ — Constructive and digital

Digital (23, 36, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 18, 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]

(23, 23+13, 73)-Net over F₃ — Digital

Digital (23, 36, 73)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(23, 23+13, 903)-Net in Base 3 — Upper bound on s

There is no (23, 36, 904)-net in base 3, because

1 times m-reduction [i] would yield (23, 35, 904)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 50306 461135 424817 > 3³⁵ [i]