MinT - Best Known (137−66, 137, s)-Nets in Base 9

Best Known (137−66, 137, s)-Nets in Base 9

(137−66, 137, 232)-Net over F₉ — Constructive and digital

Digital (71, 137, 232)-net over F₉, using

1 times m-reduction [i] based on digital (71, 138, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 69, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(137−66, 137, 301)-Net over F₉ — Digital

Digital (71, 137, 301)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−66, 137, 15039)-Net in Base 9 — Upper bound on s

There is no (71, 137, 15040)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53903 796943 777475 030642 846360 013537 202274 878585 505110 056431 294262 766465 663930 997426 526081 959602 671870 914231 875867 789032 907986 834945 > 9¹³⁷ [i]