MinT - Best Known (15, 28, s)-Nets in Base 3

Best Known (15, 28, s)-Nets in Base 3

(15, 28, 32)-Net over F₃ — Constructive and digital

Digital (15, 28, 32)-net over F₃, using

trace code for nets [i] based on digital (1, 14, 16)-net over F₉, using
- net from sequence [i] based on digital (1, 15)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
    - a function field by GarcÃa and Quoos [i]

(15, 28, 204)-Net in Base 3 — Upper bound on s

There is no (15, 28, 205)-net in base 3, because

1 times m-reduction [i] would yield (15, 27, 205)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 720059 731473 > 3²⁷ [i]