MinT - Best Known (46−39, 46, s)-Nets in Base 64

Best Known (46−39, 46, s)-Nets in Base 64

(46−39, 46, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 46, 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]

(46−39, 46, 2376)-Net in Base 64 — Upper bound on s

There is no (7, 46, 2377)-net in base 64, because

1 times m-reduction [i] would yield (7, 45, 2377)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 1901 653420 128729 015992 169972 366321 967699 848383 036315 248814 405279 873652 109242 152416 > 64⁴⁵ [i]