MinT - Best Known (55−33, 55, s)-Nets in Base 9

Best Known (55−33, 55, s)-Nets in Base 9

(55−33, 55, 78)-Net over F₉ — Constructive and digital

Digital (22, 55, 78)-net over F₉, using

net from sequence [i] based on digital (22, 77)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
  - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(55−33, 55, 88)-Net over F₉ — Digital

Digital (22, 55, 88)-net over F₉, using

t-expansion [i] based on digital (21, 55, 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]

(55−33, 55, 1403)-Net in Base 9 — Upper bound on s

There is no (22, 55, 1404)-net in base 9, because

1 times m-reduction [i] would yield (22, 54, 1404)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3415 527614 169591 477535 495554 153578 693022 796534 657537 > 9⁵⁴ [i]