MinT - Best Known (89−54, 89, s)-Nets in Base 64

Best Known (89−54, 89, s)-Nets in Base 64

(89−54, 89, 513)-Net over F₆₄ — Constructive and digital

Digital (35, 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]

(89−54, 89, 155859)-Net in Base 64 — Upper bound on s

There is no (35, 89, 155860)-net in base 64, because

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]