MinT - Best Known (58, 58+41, s)-Nets in Base 9

Best Known (58, 58+41, s)-Nets in Base 9

(58, 58+41, 344)-Net over F₉ — Constructive and digital

Digital (58, 99, 344)-net over F₉, using

3 times m-reduction [i] based on digital (58, 102, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 51, 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]

(58, 58+41, 461)-Net over F₉ — Digital

Digital (58, 99, 461)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+41, 49192)-Net in Base 9 — Upper bound on s

There is no (58, 99, 49193)-net in base 9, because

1 times m-reduction [i] would yield (58, 98, 49193)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3279 893108 676890 198647 160349 589179 921386 845162 894150 485613 433508 885660 364257 335123 587976 368929 > 9⁹⁸ [i]