  Electronic transport through chaotic quantum dots exhibits universal
behaviour which can be understood through the semiclassical approximation.
Within the approximation, transport moments reduce to codifying classical
correlations between scattering trajectories. These can be represented as
ribbon graphs and we develop an algorithmic combinatorial method to generate
all such graphs with a given genus. This provides an expansion of the linear
transport moments for systems both with and without time reversal symmetry. The
computational implementation is then able to progress several orders higher
than previous semiclassical formulae as well as those derived from an
asymptotic expansion of random matrix results. The patterns observed also
suggest a general form for the higher orders.
