MinT - Best Known (72−62, 72, s)-Nets in Base 64

Best Known (72−62, 72, s)-Nets in Base 64

(72−62, 72, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 72, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 72, 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]

(72−62, 72, 225)-Net over F₆₄ — Digital

Digital (10, 72, 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]

(72−62, 72, 3072)-Net in Base 64 — Upper bound on s

There is no (10, 72, 3073)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11132 928969 383130 308293 101768 154552 049937 245230 632955 601959 476789 048576 396982 010819 629832 261622 756257 946825 443053 299441 860915 891200 > 64⁷² [i]