MinT - Best Known (37, 37+53, s)-Nets in Base 64

Best Known (37, 37+53, s)-Nets in Base 64

(37, 37+53, 513)-Net over F₆₄ — Constructive and digital

Digital (37, 90, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 90, 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]

(37, 37+53, 540)-Net over F₆₄ — Digital

Digital (37, 90, 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]

(37, 37+53, 255048)-Net in Base 64 — Upper bound on s

There is no (37, 90, 255049)-net in base 64, because

1 times m-reduction [i] would yield (37, 89, 255049)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56236 873537 356359 563064 263990 851103 052516 699805 905996 636269 577992 533618 460665 496179 118267 685378 458825 215769 498238 520109 372407 197617 903876 318607 989552 002300 948256 > 64⁸⁹ [i]