MinT - Best Known (90−57, 90, s)-Nets in Base 64

Best Known (90−57, 90, s)-Nets in Base 64

(90−57, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (33, 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]

(90−57, 90, 98781)-Net in Base 64 — Upper bound on s

There is no (33, 90, 98782)-net in base 64, because

1 times m-reduction [i] would yield (33, 89, 98782)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56245 760983 020594 082756 681901 075057 572975 743628 042671 799767 424261 303932 303495 541982 090487 022108 208441 341854 082207 756817 503907 219712 637982 521472 551441 558516 458121 > 64⁸⁹ [i]