MinT - Best Known (58, 58+25, s)-Nets in Base 9

Best Known (58, 58+25, s)-Nets in Base 9

(58, 58+25, 740)-Net over F₉ — Constructive and digital

Digital (58, 83, 740)-net over F₉, using

1 times m-reduction [i] based on digital (58, 84, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 42, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(58, 58+25, 2457)-Net over F₉ — Digital

Digital (58, 83, 2457)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+25, 2192437)-Net in Base 9 — Upper bound on s

There is no (58, 83, 2192438)-net in base 9, because

1 times m-reduction [i] would yield (58, 82, 2192438)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 769649 951764 857088 668950 016263 623962 993303 038663 876668 105066 008106 752975 694529 > 9⁸² [i]