MinT - Best Known (8, 54, s)-Nets in Base 64

Best Known (8, 54, s)-Nets in Base 64

(8, 54, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 54, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 54, 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, 54, 2593)-Net in Base 64 — Upper bound on s

There is no (8, 54, 2594)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 34 456992 493997 683297 671317 064510 264668 208607 785311 639444 444808 518234 543249 970358 456865 467945 483888 > 64⁵⁴ [i]