MinT - Best Known (109−42, 109, s)-Nets in Base 9

Best Known (109−42, 109, s)-Nets in Base 9

(109−42, 109, 344)-Net over F₉ — Constructive and digital

Digital (67, 109, 344)-net over F₉, using

11 times m-reduction [i] based on digital (67, 120, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 60, 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]

(109−42, 109, 715)-Net over F₉ — Digital

Digital (67, 109, 715)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−42, 109, 97346)-Net in Base 9 — Upper bound on s

There is no (67, 109, 97347)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 102 920647 710246 436962 636548 092248 580527 823725 781915 537536 125865 014136 915522 773853 506289 222081 827285 012217 > 9¹⁰⁹ [i]