MinT - Best Known (102−33, 102, s)-Nets in Base 9

Best Known (102−33, 102, s)-Nets in Base 9

(102−33, 102, 740)-Net over F₉ — Constructive and digital

Digital (69, 102, 740)-net over F₉, using

4 times m-reduction [i] based on digital (69, 106, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 53, 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]

(102−33, 102, 1776)-Net over F₉ — Digital

Digital (69, 102, 1776)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−33, 102, 897635)-Net in Base 9 — Upper bound on s

There is no (69, 102, 897636)-net in base 9, because

1 times m-reduction [i] would yield (69, 101, 897636)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 390550 523476 577687 207058 445754 641765 947395 584395 253642 875236 681124 865506 780430 235611 732635 139585 > 9¹⁰¹ [i]