MinT - Best Known (57, 94, s)-Nets in Base 9

Best Known (57, 94, s)-Nets in Base 9

(57, 94, 344)-Net over F₉ — Constructive and digital

Digital (57, 94, 344)-net over F₉, using

6 times m-reduction [i] based on digital (57, 100, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 50, 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]

(57, 94, 572)-Net over F₉ — Digital

Digital (57, 94, 572)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 94, 80396)-Net in Base 9 — Upper bound on s

There is no (57, 94, 80397)-net in base 9, because

1 times m-reduction [i] would yield (57, 93, 80397)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55544 502060 128390 877367 619750 756812 690095 188463 639508 158100 726733 955835 350745 529021 341713 > 9⁹³ [i]