Summary: The neighbour method of Kneser can be adapted to the Hermitian case. Generalizing results of D. W. Hoffmann
[Manuscr. Math. 71, No. 4, 399–429 (1991; Zbl 0729.11020
)], we show that it can be used to classify any genus in a Hermitian space of dimension
by neighbour steps at suitable primes. The method was implemented for positive definite Hermitian lattices (not necessarily free) over
. A table of class numbers of unimodular genera and the largest minima attained in those genera is given. We also describe a generalization of the LLL-algorithm to lattices in positive Hermitian spaces over number fields.