MinT - Best Known (89−53, 89, s)-Nets in Base 64

Best Known (89−53, 89, s)-Nets in Base 64

(89−53, 89, 513)-Net over F₆₄ — Constructive and digital

Digital (36, 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]

(89−53, 89, 217345)-Net in Base 64 — Upper bound on s

There is no (36, 89, 217346)-net in base 64, because

1 times m-reduction [i] would yield (36, 88, 217346)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 878 716997 320088 727997 733032 802324 550910 330913 457010 754572 764063 243016 722893 492868 447182 369395 087101 707549 396782 773162 363122 753313 479988 291957 181311 037907 285632 > 64⁸⁸ [i]