MinT - Best Known (120−56, 120, s)-Nets in Base 9

Best Known (120−56, 120, s)-Nets in Base 9

(120−56, 120, 300)-Net over F₉ — Constructive and digital

Digital (64, 120, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 60, 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]

(120−56, 120, 308)-Net over F₉ — Digital

Digital (64, 120, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 60, 154)-net over F₈₁, using
- net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
    - a curve from the manYPoints database [i]

(120−56, 120, 17342)-Net in Base 9 — Upper bound on s

There is no (64, 120, 17343)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 234204 946982 796917 473312 155973 981879 026737 713040 128369 752061 963718 277070 998453 249306 958202 356417 832201 045437 585185 > 9¹²⁰ [i]