MinT - Best Known (90−49, 90, s)-Nets in Base 16

Best Known (90−49, 90, s)-Nets in Base 16

(90−49, 90, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 90, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 90, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(90−49, 90, 19065)-Net in Base 16 — Upper bound on s

There is no (41, 90, 19066)-net in base 16, because

1 times m-reduction [i] would yield (41, 89, 19066)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 146849 517029 542852 048558 671203 264935 906677 850001 739219 008357 215596 878962 363438 210382 826204 331880 838299 629111 > 16⁸⁹ [i]