@article{Belabas2008SmallGO,
title={Small generators of the ideal class group},
author={Karim Belabas and Francisco Diaz y Diaz and Eduardo Friedman},
journal={Math. Comput.},
year={2008},
volume={77},
pages={1185-1197}
}

Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group C K of a number field K can be generated by the prime ideals of K having norm smaller than 12 ( log |Discriminant(K)| )2 . This result is essential for the computation of the class group and units of K by Buchmann’s algorithm, currently the fastest known. However, once C K has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved… CONTINUE READING