Eikonal gluon radiation at finite-Nc beyond 2 loops

We present first calculations of QCD matrix-elements in perturbation theory at finite Nc beyond 2 loops in the eikonal approximation for e+ e- annihilation processes. For the emission of n soft energy-ordered gluons we solve both the colour and kinematic structures at a given order in perturbation theory by means of a Mathematica program that relies solely on a recently developed Mathematica code, ColorMath, that evaluates the trace of products of colour matrices. At large Nc, our squared amplitudes reduce to those already known in the literature.