MinT - Best Known (33, 33+58, s)-Nets in Base 64

Best Known (33, 33+58, s)-Nets in Base 64

(33, 33+58, 513)-Net over F₆₄ — Constructive and digital

Digital (33, 91, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 91, 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]

(33, 33+58, 86174)-Net in Base 64 — Upper bound on s

There is no (33, 91, 86175)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 230 413394 780337 022306 903217 430196 920770 336081 214923 993185 148881 980311 130555 127828 735377 643092 169635 998020 603631 924610 004598 014275 400368 001283 523087 836318 374013 708722 > 64⁹¹ [i]