MinT - Best Known (77−20, 77, s)-Nets in Base 9

Best Known (77−20, 77, s)-Nets in Base 9

(77−20, 77, 740)-Net over F₉ — Constructive and digital

Digital (57, 77, 740)-net over F₉, using

5 times m-reduction [i] based on digital (57, 82, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 41, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(77−20, 77, 7309)-Net over F₉ — Digital

Digital (57, 77, 7309)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−20, 77, large)-Net in Base 9 — Upper bound on s

There is no (57, 77, large)-net in base 9, because

18 times m-reduction [i] would yield (57, 59, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]