MinT - Best Known (134−58, 134, s)-Nets in Base 9

Best Known (134−58, 134, s)-Nets in Base 9

(134−58, 134, 344)-Net over F₉ — Constructive and digital

Digital (76, 134, 344)-net over F₉, using

4 times m-reduction [i] based on digital (76, 138, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 69, 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]

(134−58, 134, 488)-Net over F₉ — Digital

Digital (76, 134, 488)-net over F₉, using

trace code for nets [i] based on digital (9, 67, 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]

(134−58, 134, 37418)-Net in Base 9 — Upper bound on s

There is no (76, 134, 37419)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 73 905023 723730 875688 547972 312383 733354 410601 849110 655170 756486 085987 137563 792275 079383 563613 311166 292839 425245 828054 277289 157113 > 9¹³⁴ [i]