MinT - Best Known (60−53, 60, s)-Nets in Base 64

Best Known (60−53, 60, s)-Nets in Base 64

(60−53, 60, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 60, 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]

(60−53, 60, 2088)-Net in Base 64 — Upper bound on s

There is no (7, 60, 2089)-net in base 64, because

1 times m-reduction [i] would yield (7, 59, 2089)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 36739 357426 060461 878222 495487 528375 488895 374039 007423 097363 316149 553179 443773 322157 199494 884702 141469 008304 > 64⁵⁹ [i]