Integer transfinite diameter and polynomials with small Mahler measure

In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in $\mathbb{C}$ give very good bounds for coefficients of polynomials with small Mahler measure. By this way, we give the list of all monic irreducible primitive polynomials of $\mathbb{Z}[X]$ of degree at most $36$ with Mahler measure less than $1.\,324...$ and of degree $38$ and $40$ with Mahler measure less than $1.\,31$.