MinT - Best Known (27−17, 27, s)-Nets in Base 3

Best Known (27−17, 27, s)-Nets in Base 3

(27−17, 27, 19)-Net over F₃ — Constructive and digital

Digital (10, 27, 19)-net over F₃, using

t-expansion [i] based on digital (9, 27, 19)-net over F₃, using
- net from sequence [i] based on digital (9, 18)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
    - an explicitly constructive algebraic function field [i]

(27−17, 27, 20)-Net over F₃ — Digital

Digital (10, 27, 20)-net over F₃, using

net from sequence [i] based on digital (10, 19)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 10 and N(F) ≥ 20, using
  - a curve from the manYPoints database [i]

(27−17, 27, 59)-Net in Base 3 — Upper bound on s

There is no (10, 27, 60)-net in base 3, because

1 times m-reduction [i] would yield (10, 26, 60)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 629569 558465 > 3²⁶ [i]