MinT - Best Known (133−60, 133, s)-Nets in Base 9

Best Known (133−60, 133, s)-Nets in Base 9

(133−60, 133, 320)-Net over F₉ — Constructive and digital

Digital (73, 133, 320)-net over F₉, using

3 times m-reduction [i] based on digital (73, 136, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 68, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(133−60, 133, 390)-Net over F₉ — Digital

Digital (73, 133, 390)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−60, 133, 25577)-Net in Base 9 — Upper bound on s

There is no (73, 133, 25578)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 209711 068527 622932 192940 139367 975984 228558 998030 400360 252546 841804 724014 086401 844443 354965 383818 742891 275385 532277 646040 882337 > 9¹³³ [i]