MinT - Best Known (88−77, 88, s)-Nets in Base 64

Best Known (88−77, 88, s)-Nets in Base 64

(88−77, 88, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 88, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 88, 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]

(88−77, 88, 225)-Net over F₆₄ — Digital

Digital (11, 88, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 88, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(88−77, 88, 3236)-Net in Base 64 — Upper bound on s

There is no (11, 88, 3237)-net in base 64, because

1 times m-reduction [i] would yield (11, 87, 3237)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 766997 505234 980994 700406 562829 112176 869016 626619 951267 026846 242561 766744 002870 226891 475338 280036 640365 598599 967889 543180 722335 684636 707261 910236 227319 507264 > 64⁸⁷ [i]