MinT - Best Known (50−43, 50, s)-Nets in Base 64

Best Known (50−43, 50, s)-Nets in Base 64

(50−43, 50, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 50, 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]

(50−43, 50, 2246)-Net in Base 64 — Upper bound on s

There is no (7, 50, 2247)-net in base 64, because

1 times m-reduction [i] would yield (7, 49, 2247)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 31862 390707 591680 738350 912897 023435 406221 691256 634741 444100 007177 211972 591793 659711 191592 > 64⁴⁹ [i]