MinT - Best Known (143−59, 143, s)-Nets in Base 9

Best Known (143−59, 143, s)-Nets in Base 9

(143−59, 143, 344)-Net over F₉ — Constructive and digital

Digital (84, 143, 344)-net over F₉, using

t-expansion [i] based on digital (82, 143, 344)-net over F₉, using
- 7 times m-reduction [i] based on digital (82, 150, 344)-net over F₉, using
  - trace code for nets [i] based on digital (7, 75, 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]

(143−59, 143, 629)-Net over F₉ — Digital

Digital (84, 143, 629)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−59, 143, 68614)-Net in Base 9 — Upper bound on s

There is no (84, 143, 68615)-net in base 9, because

1 times m-reduction [i] would yield (84, 142, 68615)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3180 227862 807676 789455 656726 789771 315760 318430 683594 559858 562936 162066 053426 985772 672102 117927 734359 003421 364201 371629 265264 099090 747481 > 9¹⁴² [i]