MinT - Best Known (90−36, 90, s)-Nets in Base 9

Best Known (90−36, 90, s)-Nets in Base 9

(90−36, 90, 344)-Net over F₉ — Constructive and digital

Digital (54, 90, 344)-net over F₉, using

4 times m-reduction [i] based on digital (54, 94, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 47, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(90−36, 90, 512)-Net over F₉ — Digital

Digital (54, 90, 512)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−36, 90, 55740)-Net in Base 9 — Upper bound on s

There is no (54, 90, 55741)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 195922 406888 495880 759187 073073 265110 034908 059297 346946 112356 038661 007285 926741 161233 > 9⁹⁰ [i]