MinT - Best Known (52−45, 52, s)-Nets in Base 64

Best Known (52−45, 52, s)-Nets in Base 64

(52−45, 52, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 52, 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]

(52−45, 52, 2200)-Net in Base 64 — Upper bound on s

There is no (7, 52, 2201)-net in base 64, because

1 times m-reduction [i] would yield (7, 51, 2201)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 131 613451 831323 690167 245447 429193 842790 820803 629841 420396 294341 212817 465131 024387 348253 430836 > 64⁵¹ [i]