MinT - Best Known (109−41, 109, s)-Nets in Base 9

Best Known (109−41, 109, s)-Nets in Base 9

(109−41, 109, 448)-Net over F₉ — Constructive and digital

Digital (68, 109, 448)-net over F₉, using

1 times m-reduction [i] based on digital (68, 110, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 55, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(109−41, 109, 805)-Net over F₉ — Digital

Digital (68, 109, 805)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−41, 109, 147601)-Net in Base 9 — Upper bound on s

There is no (68, 109, 147602)-net in base 9, because

1 times m-reduction [i] would yield (68, 108, 147602)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 434734 392880 257829 044400 464790 063269 869746 254125 739319 994864 043594 840492 331370 460251 857539 667471 066561 > 9¹⁰⁸ [i]