MinT - Best Known (38, 38+53, s)-Nets in Base 64

Best Known (38, 38+53, s)-Nets in Base 64

(38, 38+53, 513)-Net over F₆₄ — Constructive and digital

Digital (38, 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]

(38, 38+53, 540)-Net over F₆₄ — Digital

Digital (38, 91, 540)-net over F₆₄, using

t-expansion [i] based on digital (37, 91, 540)-net over F₆₄, using
- net from sequence [i] based on digital (37, 539)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 37 and N(F) ≥ 540, using
    - a curve from the manYPoints database [i]

(38, 38+53, 299292)-Net in Base 64 — Upper bound on s

There is no (38, 91, 299293)-net in base 64, because

1 times m-reduction [i] would yield (38, 90, 299293)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 599423 585789 665332 737028 497581 368308 531740 665486 597794 560703 955907 387455 065286 946988 870807 088547 553045 358418 482840 894870 318113 758805 198859 034697 377528 940416 473370 > 64⁹⁰ [i]