MinT - Best Known (7, 7+63, s)-Nets in Base 64

Best Known (7, 7+63, s)-Nets in Base 64

(7, 7+63, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 70, 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, 7+63, 2049)-Net in Base 64 — Upper bound on s

There is no (7, 70, 2050)-net in base 64, because

1 times m-reduction [i] would yield (7, 69, 2050)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 42669 242388 304829 351140 260625 542594 038180 414286 148218 830407 832796 790882 934036 677099 542545 691158 170446 071063 228875 968957 432832 > 64⁶⁹ [i]