The theory of group codes simplifies the construction of good rotationally invariant trellis codes for the additive white Gaussian noise channel. New geometrically uniform trellis codes, with spectral efficiency 3 bits/2D, based on multidimensional L/spl times/16-PSK constellations in 4, 6, and 8 dimensions, obtained by group trellis codes over nonbinary groups of the kind Z/sub 16//sup L/, are presented. Most of the codes improve, in terms of asymptotic gain and rotational invariance, the best codes known so far in the literature.ETX