MinT - Best Known (49−41, 49, s)-Nets in Base 64

Best Known (49−41, 49, s)-Nets in Base 64

(49−41, 49, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 49, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 49, 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]

(49−41, 49, 2839)-Net in Base 64 — Upper bound on s

There is no (8, 49, 2840)-net in base 64, because

1 times m-reduction [i] would yield (8, 48, 2840)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 497 744169 914911 455772 710785 003939 982864 600203 719646 998953 881334 395554 708253 659931 669851 > 64⁴⁸ [i]