MinT - Best Known (73−33, 73, s)-Nets in Base 9

Best Known (73−33, 73, s)-Nets in Base 9

(73−33, 73, 232)-Net over F₉ — Constructive and digital

Digital (40, 73, 232)-net over F₉, using

3 times m-reduction [i] based on digital (40, 76, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 38, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(73−33, 73, 272)-Net over F₉ — Digital

Digital (40, 73, 272)-net over F₉, using

1 times m-reduction [i] based on digital (40, 74, 272)-net over F₉, using
- trace code for nets [i] based on digital (3, 37, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(73−33, 73, 16722)-Net in Base 9 — Upper bound on s

There is no (40, 73, 16723)-net in base 9, because

1 times m-reduction [i] would yield (40, 72, 16723)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 917123 504760 094257 165310 634158 275068 973360 404655 716539 769157 463425 > 9⁷² [i]