MinT - Best Known (32−23, 32, s)-Nets in Base 9

Best Known (32−23, 32, s)-Nets in Base 9

(32−23, 32, 40)-Net over F₉ — Constructive and digital

Digital (9, 32, 40)-net over F₉, using

t-expansion [i] based on digital (8, 32, 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]

(32−23, 32, 48)-Net over F₉ — Digital

Digital (9, 32, 48)-net over F₉, using

net from sequence [i] based on digital (9, 47)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 9 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(32−23, 32, 293)-Net in Base 9 — Upper bound on s

There is no (9, 32, 294)-net in base 9, because

1 times m-reduction [i] would yield (9, 31, 294)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 385892 545231 794186 116873 667025 > 9³¹ [i]