MinT - Best Known (60−27, 60, s)-Nets in Base 9

Best Known (60−27, 60, s)-Nets in Base 9

(60−27, 60, 232)-Net over F₉ — Constructive and digital

Digital (33, 60, 232)-net over F₉, using

2 times m-reduction [i] based on digital (33, 62, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 31, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(60−27, 60, 272)-Net over F₉ — Digital

Digital (33, 60, 272)-net over F₉, using

trace code for nets [i] based on digital (3, 30, 136)-net over F₈₁, using
- net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(60−27, 60, 15166)-Net in Base 9 — Upper bound on s

There is no (33, 60, 15167)-net in base 9, because

1 times m-reduction [i] would yield (33, 59, 15167)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 199 720502 932403 397660 324050 993801 463066 523875 987610 198425 > 9⁵⁹ [i]