MinT - Best Known (80, 150, s)-Nets in Base 9

Best Known (80, 150, s)-Nets in Base 9

(80, 150, 320)-Net over F₉ — Constructive and digital

Digital (80, 150, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 75, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(80, 150, 373)-Net over F₉ — Digital

Digital (80, 150, 373)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 150, 21347)-Net in Base 9 — Upper bound on s

There is no (80, 150, 21348)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136970 211771 197451 069901 801059 856434 918910 535887 204752 418406 343344 759898 720086 586497 064938 789704 861909 788756 024768 966225 095663 971110 698271 838433 > 9¹⁵⁰ [i]