MinT - Best Known (90−61, 90, s)-Nets in Base 64

Best Known (90−61, 90, s)-Nets in Base 64

(90−61, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (29, 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]

(90−61, 90, 43614)-Net in Base 64 — Upper bound on s

There is no (29, 90, 43615)-net in base 64, because

1 times m-reduction [i] would yield (29, 89, 43615)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56247 779688 174242 751851 060545 310740 344048 886389 325616 807984 137079 050259 933226 264779 425057 913543 280401 180255 604680 144591 589361 303542 419695 169742 827210 247060 515845 > 64⁸⁹ [i]