MinT - Best Known (90−75, 90, s)-Nets in Base 64

Best Known (90−75, 90, s)-Nets in Base 64

(90−75, 90, 177)-Net over F₆₄ — Constructive and digital

Digital (15, 90, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 90, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(90−75, 90, 258)-Net over F₆₄ — Digital

Digital (15, 90, 258)-net over F₆₄, using

net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
  - a curve from the manYPoints database [i]

(90−75, 90, 5123)-Net in Base 64 — Upper bound on s

There is no (15, 90, 5124)-net in base 64, because

1 times m-reduction [i] would yield (15, 89, 5124)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56304 644078 980970 011734 692557 196303 496432 364110 020985 732875 138023 376344 957667 744953 499411 807167 229980 699195 381024 031557 321265 172296 329938 303266 014951 973317 822720 > 64⁸⁹ [i]