MinT - Best Known (55, 55+35, s)-Nets in Base 9

Best Known (55, 55+35, s)-Nets in Base 9

(55, 55+35, 344)-Net over F₉ — Constructive and digital

Digital (55, 90, 344)-net over F₉, using

6 times m-reduction [i] based on digital (55, 96, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 48, 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]

(55, 55+35, 585)-Net over F₉ — Digital

Digital (55, 90, 585)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+35, 88827)-Net in Base 9 — Upper bound on s

There is no (55, 90, 88828)-net in base 9, because

1 times m-reduction [i] would yield (55, 89, 88828)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 465463 857167 723733 401317 613015 611392 518142 521449 756871 944276 149200 734392 969289 507297 > 9⁸⁹ [i]