MinT - Best Known (74, 74+66, s)-Nets in Base 9

Best Known (74, 74+66, s)-Nets in Base 9

(74, 74+66, 300)-Net over F₉ — Constructive and digital

Digital (74, 140, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 70, 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]

(74, 74+66, 336)-Net over F₉ — Digital

Digital (74, 140, 336)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+66, 18369)-Net in Base 9 — Upper bound on s

There is no (74, 140, 18370)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 316359 553503 903062 117925 109128 858055 794852 953264 324183 167947 331150 855856 379819 094650 765863 728664 537950 376037 801110 211023 197904 505873 > 9¹⁴⁰ [i]