MinT - Best Known (81−35, 81, s)-Nets in Base 9

Best Known (81−35, 81, s)-Nets in Base 9

(81−35, 81, 320)-Net over F₉ — Constructive and digital

Digital (46, 81, 320)-net over F₉, using

1 times m-reduction [i] based on digital (46, 82, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 41, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(81−35, 81, 334)-Net over F₉ — Digital

Digital (46, 81, 334)-net over F₉, using

1 times m-reduction [i] based on digital (46, 82, 334)-net over F₉, using
- trace code for nets [i] based on digital (5, 41, 167)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

(81−35, 81, 27749)-Net in Base 9 — Upper bound on s

There is no (46, 81, 27750)-net in base 9, because

1 times m-reduction [i] would yield (46, 80, 27750)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21858 736790 089614 494138 162517 918583 384502 798739 644668 651488 066590 856777 777201 > 9⁸⁰ [i]