MinT - Best Known (136−60, 136, s)-Nets in Base 9

Best Known (136−60, 136, s)-Nets in Base 9

(136−60, 136, 344)-Net over F₉ — Constructive and digital

Digital (76, 136, 344)-net over F₉, using

2 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]

(136−60, 136, 452)-Net over F₉ — Digital

Digital (76, 136, 452)-net over F₉, using

trace code for nets [i] based on digital (8, 68, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(136−60, 136, 31867)-Net in Base 9 — Upper bound on s

There is no (76, 136, 31868)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 5986 068404 781121 644170 980688 662976 671804 461936 524416 320239 321184 135618 123711 909938 620892 755336 257720 517979 600952 800328 664721 612993 > 9¹³⁶ [i]