MinT - Best Known (89−32, 89, s)-Nets in Base 9

Best Known (89−32, 89, s)-Nets in Base 9

(89−32, 89, 344)-Net over F₉ — Constructive and digital

Digital (57, 89, 344)-net over F₉, using

11 times m-reduction [i] based on digital (57, 100, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 50, 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]

(89−32, 89, 868)-Net over F₉ — Digital

Digital (57, 89, 868)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−32, 89, 172742)-Net in Base 9 — Upper bound on s

There is no (57, 89, 172743)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 464662 522855 680283 444587 532467 457335 866829 093122 982714 158533 980000 121064 379125 230465 > 9⁸⁹ [i]