MinT - Best Known (99−35, 99, s)-Nets in Base 9

Best Known (99−35, 99, s)-Nets in Base 9

(99−35, 99, 448)-Net over F₉ — Constructive and digital

Digital (64, 99, 448)-net over F₉, using

3 times m-reduction [i] based on digital (64, 102, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 51, 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]

(99−35, 99, 1033)-Net over F₉ — Digital

Digital (64, 99, 1033)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−35, 99, 284293)-Net in Base 9 — Upper bound on s

There is no (64, 99, 284294)-net in base 9, because

1 times m-reduction [i] would yield (64, 98, 284294)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3279 253548 968004 721426 034689 012227 945897 508492 166853 899031 952438 929355 932377 144674 470924 206385 > 9⁹⁸ [i]