We present an algorithm producing all rational functions $f$ with prescribed $n+1$ Taylor coefficients at the origin and such that $||f||_\infty \le 1$ and $\deg f \le k$ for every fixed $k\ge n$. The case where $k<n$ is also discussed.
"An algorithm for finding low degree rational solutions to the Schur coefficient problem." Funct. Approx. Comment. Math. 42 (1) 37 - 49, March 2010. https://doi.org/10.7169/facm/1269437067