MinT - Best Known (7, 40, s)-Nets in Base 64

Best Known (7, 40, s)-Nets in Base 64

(7, 40, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 40, 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]

(7, 40, 2719)-Net in Base 64 — Upper bound on s

There is no (7, 40, 2720)-net in base 64, because

1 times m-reduction [i] would yield (7, 39, 2720)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 27650 348595 686246 489772 982388 841051 662056 180346 621516 918917 867823 302507 > 64³⁹ [i]