MinT - Best Known (30, 89, s)-Nets in Base 64

Best Known (30, 89, s)-Nets in Base 64

(30, 89, 513)-Net over F₆₄ — Constructive and digital

Digital (30, 89, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 89, 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]

(30, 89, 56039)-Net in Base 64 — Upper bound on s

There is no (30, 89, 56040)-net in base 64, because

1 times m-reduction [i] would yield (30, 88, 56040)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 879 087369 421488 561128 199122 498898 585565 458234 186802 230260 879695 622250 009628 170890 650524 364323 250200 893116 796274 924941 728915 074918 961068 201705 940814 844711 200932 > 64⁸⁸ [i]