MinT - Best Known (7, 7+37, s)-Nets in Base 64

Best Known (7, 7+37, s)-Nets in Base 64

(7, 7+37, 177)-Net over F₆₄ — Constructive and digital

Digital (7, 44, 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]

(7, 7+37, 2466)-Net in Base 64 — Upper bound on s

There is no (7, 44, 2467)-net in base 64, because

1 times m-reduction [i] would yield (7, 43, 2467)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 466233 541397 088467 531977 780996 695813 560734 401767 643820 286348 963775 416065 236286 > 64⁴³ [i]