MinT - Best Known (74, 132, s)-Nets in Base 8

Best Known (74, 132, s)-Nets in Base 8

(74, 132, 354)-Net over F₈ — Constructive and digital

Digital (74, 132, 354)-net over F₈, using

2 times m-reduction [i] based on digital (74, 134, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 67, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(74, 132, 375)-Net over F₈ — Digital

Digital (74, 132, 375)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 132, 21491)-Net in Base 8 — Upper bound on s

There is no (74, 132, 21492)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 161419 921152 146042 060945 602555 196098 984371 531631 511200 658515 427421 584640 124720 710696 158219 842177 997124 439458 299312 136392 > 8¹³² [i]