MinT - Best Known (11−9, 11, s)-Nets in Base 27

Best Known (11−9, 11, s)-Nets in Base 27

(11−9, 11, 48)-Net over F₂₇ — Constructive and digital

Digital (2, 11, 48)-net over F₂₇, using

net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
  - a function field by GarcÃa and Quoos [i]

(11−9, 11, 320)-Net in Base 27 — Upper bound on s

There is no (2, 11, 321)-net in base 27, because

1 times m-reduction [i] would yield (2, 10, 321)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 206 355057 092081 > 27¹⁰ [i]