MinT - Best Known (87−33, 87, s)-Nets in Base 9

Best Known (87−33, 87, s)-Nets in Base 9

(87−33, 87, 344)-Net over F₉ — Constructive and digital

Digital (54, 87, 344)-net over F₉, using

7 times m-reduction [i] based on digital (54, 94, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 47, 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]

(87−33, 87, 644)-Net over F₉ — Digital

Digital (54, 87, 644)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−33, 87, 114410)-Net in Base 9 — Upper bound on s

There is no (54, 87, 114411)-net in base 9, because

1 times m-reduction [i] would yield (54, 86, 114411)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11611 321314 268101 048902 320319 834221 888174 647448 338282 555314 223590 617685 856578 048385 > 9⁸⁶ [i]