MinT - Best Known (132−56, 132, s)-Nets in Base 8

Best Known (132−56, 132, s)-Nets in Base 8

(132−56, 132, 354)-Net over F₈ — Constructive and digital

Digital (76, 132, 354)-net over F₈, using

6 times m-reduction [i] based on digital (76, 138, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 69, 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]

(132−56, 132, 450)-Net over F₈ — Digital

Digital (76, 132, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 66, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(132−56, 132, 29179)-Net in Base 8 — Upper bound on s

There is no (76, 132, 29180)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 161540 577755 799438 243289 104794 558121 747244 339543 873528 943522 096077 035409 879002 453419 173380 204420 930373 670587 593034 901592 > 8¹³² [i]