MinT - Best Known (61−53, 61, s)-Nets in Base 64

Best Known (61−53, 61, s)-Nets in Base 64

(61−53, 61, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 61, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 61, 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]

(61−53, 61, 2453)-Net in Base 64 — Upper bound on s

There is no (8, 61, 2454)-net in base 64, because

1 times m-reduction [i] would yield (8, 60, 2454)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 361411 510137 286942 584581 808934 368673 358534 868253 457283 765395 560971 465639 637656 928292 081940 835887 897726 157664 > 64⁶⁰ [i]