MinT - Best Known (84, 150, s)-Nets in Base 9

Best Known (84, 150, s)-Nets in Base 9

(84, 150, 344)-Net over F₉ — Constructive and digital

Digital (84, 150, 344)-net over F₉, using

t-expansion [i] based on digital (82, 150, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 75, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(84, 150, 488)-Net over F₉ — Digital

Digital (84, 150, 488)-net over F₉, using

trace code for nets [i] based on digital (9, 75, 244)-net over F₈₁, using
- net from sequence [i] based on digital (9, 243)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 9 and N(F) ≥ 244, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₈₁ [i]

(84, 150, 35767)-Net in Base 9 — Upper bound on s

There is no (84, 150, 35768)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136983 339535 152823 288760 071670 513338 766948 488990 849907 090746 283434 027308 007596 477282 492815 863524 042406 234587 130557 187115 920255 752715 043199 518145 > 9¹⁵⁰ [i]