MinT - Best Known (98−43, 98, s)-Nets in Base 9

Best Known (98−43, 98, s)-Nets in Base 9

(98−43, 98, 320)-Net over F₉ — Constructive and digital

Digital (55, 98, 320)-net over F₉, using

2 times m-reduction [i] based on digital (55, 100, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 50, 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]

(98−43, 98, 380)-Net over F₉ — Digital

Digital (55, 98, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 49, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(98−43, 98, 27726)-Net in Base 9 — Upper bound on s

There is no (55, 98, 27727)-net in base 9, because

1 times m-reduction [i] would yield (55, 97, 27727)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 466443 155921 670340 322701 590702 116925 028677 911339 957329 413208 402470 242834 424255 332847 353817 > 9⁹⁷ [i]