MinT - Best Known (53−45, 53, s)-Nets in Base 64

Best Known (53−45, 53, s)-Nets in Base 64

(53−45, 53, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 53, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 53, 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]

(53−45, 53, 2660)-Net in Base 64 — Upper bound on s

There is no (8, 53, 2661)-net in base 64, because

1 times m-reduction [i] would yield (8, 52, 2661)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 8405 360631 573128 968178 427760 685623 800422 456204 545805 390724 442983 080933 812054 722959 850170 701456 > 64⁵² [i]