Euclidean minima of totally real number fields: Algorithmic determination

Source abstract

This article deals with the determination of the Euclidean minimum M ( K ) M(K) of a totally real number field K K of degree n ≥ 2 n\geq 2 , using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree 2 2 to 8 8 and small discriminants, most of which were previously unknown. Tables are given at the end of this paper.