MinT - Best Known (118−59, 118, s)-Nets in Base 9

Best Known (118−59, 118, s)-Nets in Base 9

(118−59, 118, 164)-Net over F₉ — Constructive and digital

Digital (59, 118, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 59, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(118−59, 118, 226)-Net over F₉ — Digital

Digital (59, 118, 226)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−59, 118, 10307)-Net in Base 9 — Upper bound on s

There is no (59, 118, 10308)-net in base 9, because

1 times m-reduction [i] would yield (59, 117, 10308)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4432 349916 639684 094722 155068 946971 676116 161926 176188 568109 871220 154210 328785 332566 168466 378332 284722 070660 506785 > 9¹¹⁷ [i]