MinT - Best Known (135−47, 135, s)-Nets in Base 9

Best Known (135−47, 135, s)-Nets in Base 9

(135−47, 135, 740)-Net over F₉ — Constructive and digital

Digital (88, 135, 740)-net over F₉, using

9 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 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]

(135−47, 135, 1444)-Net over F₉ — Digital

Digital (88, 135, 1444)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−47, 135, 427417)-Net in Base 9 — Upper bound on s

There is no (88, 135, 427418)-net in base 9, because

1 times m-reduction [i] would yield (88, 134, 427418)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 73 877825 267199 715337 347372 885059 642732 686083 003253 644941 413136 978420 789535 805466 613590 667327 471401 534097 984340 450794 951964 100465 > 9¹³⁴ [i]