MinT - Best Known (50, 50+23, s)-Nets in Base 9

Best Known (50, 50+23, s)-Nets in Base 9

(50, 50+23, 448)-Net over F₉ — Constructive and digital

Digital (50, 73, 448)-net over F₉, using

1 times m-reduction [i] based on digital (50, 74, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 37, 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]

(50, 50+23, 1671)-Net over F₉ — Digital

Digital (50, 73, 1671)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+23, 1081116)-Net in Base 9 — Upper bound on s

There is no (50, 73, 1081117)-net in base 9, because

1 times m-reduction [i] would yield (50, 72, 1081117)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 530293 550024 521642 328831 255070 641266 019854 715226 060242 144349 504825 > 9⁷² [i]