MinT - Best Known (30−19, 30, s)-Nets in Base 9

Best Known (30−19, 30, s)-Nets in Base 9

(30−19, 30, 40)-Net over F₉ — Constructive and digital

Digital (11, 30, 40)-net over F₉, using

t-expansion [i] based on digital (8, 30, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(30−19, 30, 55)-Net over F₉ — Digital

Digital (11, 30, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(30−19, 30, 610)-Net in Base 9 — Upper bound on s

There is no (11, 30, 611)-net in base 9, because

1 times m-reduction [i] would yield (11, 29, 611)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4731 296065 038372 691164 783065 > 9²⁹ [i]