MinT - Best Known (73−51, 73, s)-Nets in Base 9

Best Known (73−51, 73, s)-Nets in Base 9

(73−51, 73, 78)-Net over F₉ — Constructive and digital

Digital (22, 73, 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]

(73−51, 73, 88)-Net over F₉ — Digital

Digital (22, 73, 88)-net over F₉, using

t-expansion [i] based on digital (21, 73, 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]

(73−51, 73, 697)-Net in Base 9 — Upper bound on s

There is no (22, 73, 698)-net in base 9, because

1 times m-reduction [i] would yield (22, 72, 698)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 517 966118 473146 611560 654807 645003 368706 116507 522508 843019 476932 109905 > 9⁷² [i]