MinT - Best Known (90−55, 90, s)-Nets in Base 64

Best Known (90−55, 90, s)-Nets in Base 64

(90−55, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (35, 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]

(90−55, 90, 155859)-Net in Base 64 — Upper bound on s

There is no (35, 90, 155860)-net in base 64, because

1 times m-reduction [i] would yield (35, 89, 155860)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56241 695944 725971 595153 071268 012173 790515 354357 401626 274570 198940 518718 096065 024064 300014 263265 884729 754077 064603 332118 137983 561602 339727 605349 717203 035057 399016 > 64⁸⁹ [i]