MinT - Best Known (90−56, 90, s)-Nets in Base 64

Best Known (90−56, 90, s)-Nets in Base 64

(90−56, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (34, 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]

(90−56, 90, 114601)-Net in Base 64 — Upper bound on s

There is no (34, 90, 114602)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 599611 022707 094979 286068 140613 545192 132112 243259 432502 146481 410846 811900 656157 450574 946723 543322 595076 626263 531585 972905 003976 005881 443011 630902 747560 319092 372968 > 64⁹⁰ [i]