MinT - Best Known (123−54, 123, s)-Nets in Base 8

Best Known (123−54, 123, s)-Nets in Base 8

(123−54, 123, 354)-Net over F₈ — Constructive and digital

Digital (69, 123, 354)-net over F₈, using

1 times m-reduction [i] based on digital (69, 124, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 62, 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]

(123−54, 123, 355)-Net over F₈ — Digital

Digital (69, 123, 355)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−54, 123, 20277)-Net in Base 8 — Upper bound on s

There is no (69, 123, 20278)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1202 496326 326120 539129 946177 571287 622037 063122 761071 687383 297364 211242 985849 521965 676082 523875 070356 278363 524040 > 8¹²³ [i]