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

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

(64−54, 64, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 64, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 64, 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]

(64−54, 64, 225)-Net over F₆₄ — Digital

Digital (10, 64, 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]

(64−54, 64, 3300)-Net in Base 64 — Upper bound on s

There is no (10, 64, 3301)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 39 464587 699640 829723 217641 011937 471622 292697 031034 240211 543982 660682 342564 426298 891291 270821 108326 658422 111458 847600 > 64⁶⁴ [i]