MinT - Best Known (88−23, 88, s)-Nets in Base 9

Best Known (88−23, 88, s)-Nets in Base 9

(88−23, 88, 740)-Net over F₉ — Constructive and digital

Digital (65, 88, 740)-net over F₉, using

10 times m-reduction [i] based on digital (65, 98, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 49, 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]

(88−23, 88, 7437)-Net over F₉ — Digital

Digital (65, 88, 7437)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−23, 88, large)-Net in Base 9 — Upper bound on s

There is no (65, 88, large)-net in base 9, because

21 times m-reduction [i] would yield (65, 67, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]