MinT - Best Known (87−29, 87, s)-Nets in Base 9

Best Known (87−29, 87, s)-Nets in Base 9

(87−29, 87, 448)-Net over F₉ — Constructive and digital

Digital (58, 87, 448)-net over F₉, using

3 times m-reduction [i] based on digital (58, 90, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 45, 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]

(87−29, 87, 1317)-Net over F₉ — Digital

Digital (58, 87, 1317)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−29, 87, 549713)-Net in Base 9 — Upper bound on s

There is no (58, 87, 549714)-net in base 9, because

1 times m-reduction [i] would yield (58, 86, 549714)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11610 686017 169580 570174 564496 335267 098249 070267 547870 861295 403325 662628 988728 241697 > 9⁸⁶ [i]