MinT - Best Known (90−60, 90, s)-Nets in Base 64

Best Known (90−60, 90, s)-Nets in Base 64

(90−60, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (30, 90, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 90, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(90−60, 90, 50102)-Net in Base 64 — Upper bound on s

There is no (30, 90, 50103)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 600492 761068 761097 330993 262062 551966 526339 135694 764160 543221 451895 758578 537460 331009 277633 819428 028973 344132 921742 873714 968908 947671 360382 412841 501414 784670 972964 > 64⁹⁰ [i]