MinT - Best Known (145−60, 145, s)-Nets in Base 8

Best Known (145−60, 145, s)-Nets in Base 8

(145−60, 145, 354)-Net over F₈ — Constructive and digital

Digital (85, 145, 354)-net over F₈, using

11 times m-reduction [i] based on digital (85, 156, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 78, 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]

(145−60, 145, 531)-Net over F₈ — Digital

Digital (85, 145, 531)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−60, 145, 39849)-Net in Base 8 — Upper bound on s

There is no (85, 145, 39850)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 88770 873334 534227 822902 036488 053895 612754 320818 118311 536371 662345 746366 138678 257879 738507 734080 957379 501522 576831 770672 459494 722064 > 8¹⁴⁵ [i]