MinT - Best Known (81−21, 81, s)-Nets in Base 9

Best Known (81−21, 81, s)-Nets in Base 9

(81−21, 81, 740)-Net over F₉ — Constructive and digital

Digital (60, 81, 740)-net over F₉, using

7 times m-reduction [i] based on digital (60, 88, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 44, 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]

(81−21, 81, 7611)-Net over F₉ — Digital

Digital (60, 81, 7611)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−21, 81, large)-Net in Base 9 — Upper bound on s

There is no (60, 81, large)-net in base 9, because

19 times m-reduction [i] would yield (60, 62, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]