MinT - Best Known (90−71, 90, s)-Nets in Base 16

Best Known (90−71, 90, s)-Nets in Base 16

(90−71, 90, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 90, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 90, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(90−71, 90, 129)-Net over F₁₆ — Digital

Digital (19, 90, 129)-net over F₁₆, using

net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(90−71, 90, 1049)-Net in Base 16 — Upper bound on s

There is no (19, 90, 1050)-net in base 16, because

1 times m-reduction [i] would yield (19, 89, 1050)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 146786 461394 217681 532923 197512 978814 306320 888571 529679 432922 492782 243192 651220 906203 085971 022901 425085 429376 > 16⁸⁹ [i]