MinT - Best Known (24, 48, s)-Nets in Base 7

Best Known (24, 48, s)-Nets in Base 7

(24, 48, 100)-Net over F₇ — Constructive and digital

Digital (24, 48, 100)-net over F₇, using

trace code for nets [i] based on digital (0, 24, 50)-net over F₄₉, using
- net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
    - the rational function field F₄₉(x) [i]
  - Niederreiter sequence [i]

(24, 48, 2108)-Net in Base 7 — Upper bound on s

There is no (24, 48, 2109)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 36717 701184 277948 354150 443326 680863 978337 > 7⁴⁸ [i]