MinT - Best Known (130−56, 130, s)-Nets in Base 9

Best Known (130−56, 130, s)-Nets in Base 9

(130−56, 130, 344)-Net over F₉ — Constructive and digital

Digital (74, 130, 344)-net over F₉, using

4 times m-reduction [i] based on digital (74, 134, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 67, 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]

(130−56, 130, 488)-Net over F₉ — Digital

Digital (74, 130, 488)-net over F₉, using

trace code for nets [i] based on digital (9, 65, 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]

(130−56, 130, 38030)-Net in Base 9 — Upper bound on s

There is no (74, 130, 38031)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11263 397606 610281 192276 750164 099886 248710 557829 489095 725904 646569 969914 080317 262177 538275 358789 028027 251665 964387 852022 524193 > 9¹³⁰ [i]