Curves over every global field violating the local-global principle

There is an algorithm that takes as input a global field $k$ and produces a curve over $k$ violating the local-global principle. Also, given a global field $k$ and a nonnegative integer $n$, one can effectively construct a curve $X$ over $k$ such that $\#X(k)=n$. Bibl. 26 titles.