MinT - Best Known (56, 56+37, s)-Nets in Base 9

Best Known (56, 56+37, s)-Nets in Base 9

(56, 56+37, 344)-Net over F₉ — Constructive and digital

Digital (56, 93, 344)-net over F₉, using

5 times m-reduction [i] based on digital (56, 98, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 49, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(56, 56+37, 539)-Net over F₉ — Digital

Digital (56, 93, 539)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+37, 71156)-Net in Base 9 — Upper bound on s

There is no (56, 93, 71157)-net in base 9, because

1 times m-reduction [i] would yield (56, 92, 71157)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6171 303894 570761 518073 431941 834339 288116 450321 363810 034663 430128 979909 017571 839900 479889 > 9⁹² [i]