MinT - Best Known (48−41, 48, s)-Nets in Base 64

Best Known (48−41, 48, s)-Nets in Base 64

(48−41, 48, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 48, 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]

(48−41, 48, 2304)-Net in Base 64 — Upper bound on s

There is no (7, 48, 2305)-net in base 64, because

1 times m-reduction [i] would yield (7, 47, 2305)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 7 780176 695693 856679 628089 348116 763407 729251 081940 622398 532559 095193 040391 136771 813056 > 64⁴⁷ [i]