MinT - Best Known (119−45, 119, s)-Nets in Base 9

Best Known (119−45, 119, s)-Nets in Base 9

(119−45, 119, 448)-Net over F₉ — Constructive and digital

Digital (74, 119, 448)-net over F₉, using

3 times m-reduction [i] based on digital (74, 122, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 61, 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]

(119−45, 119, 844)-Net over F₉ — Digital

Digital (74, 119, 844)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−45, 119, 148571)-Net in Base 9 — Upper bound on s

There is no (74, 119, 148572)-net in base 9, because

1 times m-reduction [i] would yield (74, 118, 148572)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39872 960607 276825 021238 968874 844078 222088 226705 305334 992555 325460 988087 375014 207839 456768 505334 424514 853139 127745 > 9¹¹⁸ [i]