MinT - Best Known (123−37, 123, s)-Nets in Base 9

Best Known (123−37, 123, s)-Nets in Base 9

(123−37, 123, 740)-Net over F₉ — Constructive and digital

Digital (86, 123, 740)-net over F₉, using

17 times m-reduction [i] based on digital (86, 140, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 70, 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]

(123−37, 123, 3269)-Net over F₉ — Digital

Digital (86, 123, 3269)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−37, 123, 2771290)-Net in Base 9 — Upper bound on s

There is no (86, 123, 2771291)-net in base 9, because

1 times m-reduction [i] would yield (86, 122, 2771291)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 569699 688444 086427 785131 401125 981383 663450 139533 804031 217971 879788 095908 738268 855847 246817 106060 900769 941374 244273 > 9¹²² [i]