MinT - Best Known (28−19, 28, s)-Nets in Base 9

Best Known (28−19, 28, s)-Nets in Base 9

(28−19, 28, 40)-Net over F₉ — Constructive and digital

Digital (9, 28, 40)-net over F₉, using

t-expansion [i] based on digital (8, 28, 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]

(28−19, 28, 48)-Net over F₉ — Digital

Digital (9, 28, 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]

(28−19, 28, 372)-Net in Base 9 — Upper bound on s

There is no (9, 28, 373)-net in base 9, because

1 times m-reduction [i] would yield (9, 27, 373)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 58 416683 215911 938541 686761 > 9²⁷ [i]