MinT - Best Known (7, 7+68, s)-Nets in Base 64

Best Known (7, 7+68, s)-Nets in Base 64

(7, 7+68, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 75, 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+68, 2049)-Net in Base 64 — Upper bound on s

There is no (7, 75, 2050)-net in base 64, because

4 times m-reduction [i] would yield (7, 71, 2050)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 174 897932 169508 067743 876617 587590 285846 337967 931902 518582 008107 579166 582962 022693 674485 354050 116658 925641 998863 790174 789817 604032 > 64⁷¹ [i]