MinT - Best Known (125−46, 125, s)-Nets in Base 9

Best Known (125−46, 125, s)-Nets in Base 9

(125−46, 125, 740)-Net over F₉ — Constructive and digital

Digital (79, 125, 740)-net over F₉, using

1 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]

(125−46, 125, 1008)-Net over F₉ — Digital

Digital (79, 125, 1008)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−46, 125, 180897)-Net in Base 9 — Upper bound on s

There is no (79, 125, 180898)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 190685 633549 650466 109955 443399 360751 477420 930604 509394 479652 861775 993321 900584 713195 041812 570235 720180 515717 096100 363825 > 9¹²⁵ [i]