MinT - Best Known (143−55, 143, s)-Nets in Base 9

Best Known (143−55, 143, s)-Nets in Base 9

(143−55, 143, 740)-Net over F₉ — Constructive and digital

Digital (88, 143, 740)-net over F₉, using

1 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]

(143−55, 143, 899)-Net over F₉ — Digital

Digital (88, 143, 899)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−55, 143, 142519)-Net in Base 9 — Upper bound on s

There is no (88, 143, 142520)-net in base 9, because

1 times m-reduction [i] would yield (88, 142, 142520)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3180 101417 771868 088914 747665 523555 703359 026960 262019 617055 580677 287058 005292 265448 618399 074126 028437 328118 688625 428637 723906 893120 031809 > 9¹⁴² [i]