MinT - Best Known (54−47, 54, s)-Nets in Base 64

Best Known (54−47, 54, s)-Nets in Base 64

(54−47, 54, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 54, 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]

(54−47, 54, 2162)-Net in Base 64 — Upper bound on s

There is no (7, 54, 2163)-net in base 64, because

1 times m-reduction [i] would yield (7, 53, 2163)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 538182 811806 861979 760822 353209 403496 748998 698948 874981 372897 886626 935496 194496 677322 987591 997280 > 64⁵³ [i]