MinT - Best Known (38−27, 38, s)-Nets in Base 9

Best Known (38−27, 38, s)-Nets in Base 9

(38−27, 38, 40)-Net over F₉ — Constructive and digital

Digital (11, 38, 40)-net over F₉, using

t-expansion [i] based on digital (8, 38, 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]

(38−27, 38, 55)-Net over F₉ — Digital

Digital (11, 38, 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]

(38−27, 38, 360)-Net in Base 9 — Upper bound on s

There is no (11, 38, 361)-net in base 9, because

1 times m-reduction [i] would yield (11, 37, 361)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 204526 965282 204758 776606 947069 654057 > 9³⁷ [i]