MinT - Best Known (128−52, 128, s)-Nets in Base 8

Best Known (128−52, 128, s)-Nets in Base 8

(128−52, 128, 354)-Net over F₈ — Constructive and digital

Digital (76, 128, 354)-net over F₈, using

10 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]

(128−52, 128, 522)-Net over F₈ — Digital

Digital (76, 128, 522)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−52, 128, 42073)-Net in Base 8 — Upper bound on s

There is no (76, 128, 42074)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 412960 021096 022484 587443 752125 250131 482301 699598 104551 448094 769121 495477 794848 583092 509312 179488 644134 476054 822608 > 8¹²⁸ [i]