MinT - Best Known (31−21, 31, s)-Nets in Base 9

Best Known (31−21, 31, s)-Nets in Base 9

(31−21, 31, 40)-Net over F₉ — Constructive and digital

Digital (10, 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]

(31−21, 31, 54)-Net over F₉ — Digital

Digital (10, 31, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(31−21, 31, 406)-Net in Base 9 — Upper bound on s

There is no (10, 31, 407)-net in base 9, because

1 times m-reduction [i] would yield (10, 30, 407)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 42436 782222 742549 219266 277425 > 9³⁰ [i]