MinT - Best Known (37, 60, s)-Nets in Base 8

Best Known (37, 60, s)-Nets in Base 8

(37, 60, 354)-Net over F₈ — Constructive and digital

Digital (37, 60, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 30, 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]

(37, 60, 387)-Net over F₈ — Digital

Digital (37, 60, 387)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 60, 48944)-Net in Base 8 — Upper bound on s

There is no (37, 60, 48945)-net in base 8, because

1 times m-reduction [i] would yield (37, 59, 48945)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 191582 445114 106362 665381 496804 974543 914946 755789 413712 > 8⁵⁹ [i]