MinT - Best Known (17, 17+74, s)-Nets in Base 16

Best Known (17, 17+74, s)-Nets in Base 16

(17, 17+74, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 91, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 91, 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]

(17, 17+74, 112)-Net over F₁₆ — Digital

Digital (17, 91, 112)-net over F₁₆, using

net from sequence [i] based on digital (17, 111)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 17 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(17, 17+74, 873)-Net in Base 16 — Upper bound on s

There is no (17, 91, 874)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 38 232353 733489 294904 725652 692925 027156 935165 081543 672313 020163 569987 109132 550792 423882 293513 281299 384776 019446 > 16⁹¹ [i]