An improvement to an algorithm of Belabas, Diaz y Diaz and Friedman

In [BDyDF08] Belabas, Diaz y Diaz and Friedman show a way to determine, assuming the Generalized Riemann Hypothesis, a set of prime ideals that generate the class group of a number field. Their method is efficient because it produces a set of ideals that is smaller than earlier proved results. Here we show how to use their main result to algorithmically produce a bound that is lower than the one they prove.