MinT - Best Known (12, 12+19, s)-Nets in Base 9

Best Known (12, 12+19, s)-Nets in Base 9

(12, 12+19, 40)-Net over F₉ — Constructive and digital

Digital (12, 31, 40)-net over F₉, using

t-expansion [i] based on digital (8, 31, 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]

(12, 12+19, 56)-Net over F₉ — Digital

Digital (12, 31, 56)-net over F₉, using

net from sequence [i] based on digital (12, 55)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 12 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(12, 12+19, 780)-Net in Base 9 — Upper bound on s

There is no (12, 31, 781)-net in base 9, because

1 times m-reduction [i] would yield (12, 30, 781)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 42405 123778 771244 733922 518697 > 9³⁰ [i]