MinT - Best Known (54−25, 54, s)-Nets in Base 3

Best Known (54−25, 54, s)-Nets in Base 3

(54−25, 54, 40)-Net over F₃ — Constructive and digital

Digital (29, 54, 40)-net over F₃, using

trace code for nets [i] based on digital (2, 27, 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]

(54−25, 54, 45)-Net over F₃ — Digital

Digital (29, 54, 45)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−25, 54, 327)-Net in Base 3 — Upper bound on s

There is no (29, 54, 328)-net in base 3, because

1 times m-reduction [i] would yield (29, 53, 328)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19 935802 753105 554722 330433 > 3⁵³ [i]