MinT - Best Known (7, 7+59, s)-Nets in Base 64

Best Known (7, 7+59, s)-Nets in Base 64

(7, 7+59, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 66, 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+59, 2056)-Net in Base 64 — Upper bound on s

There is no (7, 66, 2057)-net in base 64, because

1 times m-reduction [i] would yield (7, 65, 2057)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2548 221494 782631 287233 561332 486296 848563 805633 688418 839467 351692 498650 881079 476657 358743 097728 093642 754849 524164 270080 > 64⁶⁵ [i]