MinT - Best Known (52−31, 52, s)-Nets in Base 9

Best Known (52−31, 52, s)-Nets in Base 9

(52−31, 52, 74)-Net over F₉ — Constructive and digital

Digital (21, 52, 74)-net over F₉, using

t-expansion [i] based on digital (17, 52, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(52−31, 52, 88)-Net over F₉ — Digital

Digital (21, 52, 88)-net over F₉, using

net from sequence [i] based on digital (21, 87)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
  - a curve from the manYPoints database [i]

(52−31, 52, 1400)-Net in Base 9 — Upper bound on s

There is no (21, 52, 1401)-net in base 9, because

1 times m-reduction [i] would yield (21, 51, 1401)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 650295 417989 286757 103344 950205 959411 403439 525369 > 9⁵¹ [i]