MinT - Best Known (64−57, 64, s)-Nets in Base 64

Best Known (64−57, 64, s)-Nets in Base 64

(64−57, 64, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 64, 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]

(64−57, 64, 2063)-Net in Base 64 — Upper bound on s

There is no (7, 64, 2064)-net in base 64, because

1 times m-reduction [i] would yield (7, 63, 2064)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 618067 187362 514521 783765 154255 740702 303217 615387 603989 568859 396400 638920 160654 109598 146772 542671 197954 684339 624320 > 64⁶³ [i]