MinT - Best Known (119−55, 119, s)-Nets in Base 9

Best Known (119−55, 119, s)-Nets in Base 9

(119−55, 119, 300)-Net over F₉ — Constructive and digital

Digital (64, 119, 300)-net over F₉, using

1 times m-reduction [i] based on digital (64, 120, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 60, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(119−55, 119, 319)-Net over F₉ — Digital

Digital (64, 119, 319)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−55, 119, 20200)-Net in Base 9 — Upper bound on s

There is no (64, 119, 20201)-net in base 9, because

1 times m-reduction [i] would yield (64, 118, 20201)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39903 709622 497573 010238 920301 106339 178371 268306 141066 108213 043309 870969 104743 985902 454524 648308 811620 040666 623833 > 9¹¹⁸ [i]