MinT - Best Known (123−44, 123, s)-Nets in Base 9

Best Known (123−44, 123, s)-Nets in Base 9

(123−44, 123, 740)-Net over F₉ — Constructive and digital

Digital (79, 123, 740)-net over F₉, using

3 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 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]

(123−44, 123, 1154)-Net over F₉ — Digital

Digital (79, 123, 1154)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−44, 123, 244806)-Net in Base 9 — Upper bound on s

There is no (79, 123, 244807)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 260569 246054 252902 665085 589185 116354 826083 794858 013117 832935 113567 703621 652694 502193 861835 666789 584597 328797 338065 > 9¹²³ [i]