MinT - Best Known (70, 122, s)-Nets in Base 9

Best Known (70, 122, s)-Nets in Base 9

(70, 122, 344)-Net over F₉ — Constructive and digital

Digital (70, 122, 344)-net over F₉, using

4 times m-reduction [i] based on digital (70, 126, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 63, 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]

(70, 122, 488)-Net over F₉ — Digital

Digital (70, 122, 488)-net over F₉, using

trace code for nets [i] based on digital (9, 61, 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]

(70, 122, 39594)-Net in Base 9 — Upper bound on s

There is no (70, 122, 39595)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 733798 090047 047031 828655 966830 886616 933783 028604 622510 699983 675462 054571 897455 451971 312709 354369 257306 829048 224113 > 9¹²² [i]