MinT - Best Known (98−41, 98, s)-Nets in Base 9

Best Known (98−41, 98, s)-Nets in Base 9

(98−41, 98, 344)-Net over F₉ — Constructive and digital

Digital (57, 98, 344)-net over F₉, using

2 times m-reduction [i] based on digital (57, 100, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 50, 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]

(98−41, 98, 452)-Net over F₉ — Digital

Digital (57, 98, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 49, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(98−41, 98, 44073)-Net in Base 9 — Upper bound on s

There is no (57, 98, 44074)-net in base 9, because

1 times m-reduction [i] would yield (57, 97, 44074)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 492717 465558 927331 676747 530263 842343 489007 506064 331526 602825 137228 514493 166287 344996 382401 > 9⁹⁷ [i]