MinT - Best Known (81−47, 81, s)-Nets in Base 64

Best Known (81−47, 81, s)-Nets in Base 64

(81−47, 81, 513)-Net over F₆₄ — Constructive and digital

Digital (34, 81, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 81, 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]

(81−47, 81, 286723)-Net in Base 64 — Upper bound on s

There is no (34, 81, 286724)-net in base 64, because

1 times m-reduction [i] would yield (34, 80, 286724)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 121815 300690 864979 368048 910911 478538 278794 712908 033800 638179 382615 396958 983662 622896 220425 748259 885165 238152 656037 178896 559048 505368 602497 165312 > 64⁸⁰ [i]