MinT - Best Known (86−53, 86, s)-Nets in Base 64

Best Known (86−53, 86, s)-Nets in Base 64

(86−53, 86, 513)-Net over F₆₄ — Constructive and digital

Digital (33, 86, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 86, 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]

(86−53, 86, 134502)-Net in Base 64 — Upper bound on s

There is no (33, 86, 134503)-net in base 64, because

1 times m-reduction [i] would yield (33, 85, 134503)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3352 358595 561700 356849 973146 388918 917941 970178 414442 249164 875629 902276 642727 492272 870139 185886 395062 172143 742411 277316 365962 557135 822182 768012 577249 499060 > 64⁸⁵ [i]