MinT - Best Known (50−41, 50, s)-Nets in Base 16

Best Known (50−41, 50, s)-Nets in Base 16

(50−41, 50, 65)-Net over F₁₆ — Constructive and digital

Digital (9, 50, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 50, 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]

(50−41, 50, 72)-Net over F₁₆ — Digital

Digital (9, 50, 72)-net over F₁₆, using

net from sequence [i] based on digital (9, 71)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 9 and N(F) ≥ 72, using
  - a curve from the manYPoints database [i]

(50−41, 50, 482)-Net in Base 16 — Upper bound on s

There is no (9, 50, 483)-net in base 16, because

1 times m-reduction [i] would yield (9, 49, 483)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 101447 545854 759504 610775 273077 579986 648316 592456 427490 280776 > 16⁴⁹ [i]