MinT - Best Known (45, 45+31, s)-Nets in Base 8

Best Known (45, 45+31, s)-Nets in Base 8

(45, 45+31, 354)-Net over F₈ — Constructive and digital

Digital (45, 76, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 38, 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]

(45, 45+31, 30059)-Net in Base 8 — Upper bound on s

There is no (45, 76, 30060)-net in base 8, because

1 times m-reduction [i] would yield (45, 75, 30060)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 924549 340114 903160 010207 500340 878466 652671 735366 896175 215392 654296 > 8⁷⁵ [i]