Bounds on degrees of p-adic separating polynomials

We study a discrete optimization problem introduced by Babai, Frankl, Kutin, and Štefankovič (2001), which provides bounds on degrees of polynomials with p-adically controlled behavior. Such polynomials are of particular interest because they furnish bounds on the size of set systems satisfying Frankl–Wilson-type conditions modulo prime powers, with lower degree polynomials providing better bounds. We elucidate the asymptotic structure of solutions to the optimization problem, and we also provide an improved method for finding solutions in certain circumstances.