MinT - Best Known (123−38, 123, s)-Nets in Base 9

Best Known (123−38, 123, s)-Nets in Base 9

(123−38, 123, 740)-Net over F₉ — Constructive and digital

Digital (85, 123, 740)-net over F₉, using

15 times m-reduction [i] based on digital (85, 138, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 69, 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]

(123−38, 123, 2741)-Net over F₉ — Digital

Digital (85, 123, 2741)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−38, 123, 1491375)-Net in Base 9 — Upper bound on s

There is no (85, 123, 1491376)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 148832 817381 961941 609800 956187 262882 966562 130611 009274 598258 043569 088905 846807 587653 341666 342115 165849 785795 842689 > 9¹²³ [i]