MinT - Best Known (17, 17+53, s)-Nets in Base 16

Best Known (17, 17+53, s)-Nets in Base 16

(17, 17+53, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 70, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 70, 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+53, 112)-Net over F₁₆ — Digital

Digital (17, 70, 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+53, 1089)-Net in Base 16 — Upper bound on s

There is no (17, 70, 1090)-net in base 16, because

1 times m-reduction [i] would yield (17, 69, 1090)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 123555 795386 722988 991693 764280 563295 170122 622251 984312 462229 850329 701372 828249 746976 > 16⁶⁹ [i]