MinT - Best Known (108−38, 108, s)-Nets in Base 9

Best Known (108−38, 108, s)-Nets in Base 9

(108−38, 108, 740)-Net over F₉ — Constructive and digital

Digital (70, 108, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 54, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(108−38, 108, 1136)-Net over F₉ — Digital

Digital (70, 108, 1136)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−38, 108, 263161)-Net in Base 9 — Upper bound on s

There is no (70, 108, 263162)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 434368 310003 570614 749059 742930 259079 362598 531144 931829 349822 333948 033029 153104 417465 973022 621340 972465 > 9¹⁰⁸ [i]