MinT - Best Known (90−59, 90, s)-Nets in Base 64

Best Known (90−59, 90, s)-Nets in Base 64

(90−59, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (31, 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]

(90−59, 90, 64682)-Net in Base 64 — Upper bound on s

There is no (31, 90, 64683)-net in base 64, because

1 times m-reduction [i] would yield (31, 89, 64683)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56242 775265 326584 283387 879771 696843 928902 383353 976529 202729 446519 196522 522382 278258 816300 025858 096704 963729 343744 465876 165306 395281 230290 182947 582072 853374 726960 > 64⁸⁹ [i]