MinT - Best Known (8, 8+33, s)-Nets in Base 64

Best Known (8, 8+33, s)-Nets in Base 64

(8, 8+33, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 41, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 41, 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]

(8, 8+33, 3529)-Net in Base 64 — Upper bound on s

There is no (8, 41, 3530)-net in base 64, because

1 times m-reduction [i] would yield (8, 40, 3530)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 1 772002 189249 435881 861182 520776 797277 152958 869751 761366 933289 441292 516844 > 64⁴⁰ [i]