  Subspace codes form the appropriate mathematical setting for investigating
the Koetter-Kschischang model of fault-tolerant network coding. The Main
Problem of Subspace Coding asks for the determination of a subspace code of
maximum size (proportional to the transmission rate) if the remaining
parameters are kept fixed. We describe a new approach to finding good subspace
codes, which surpasses the known size limit of lifted MRD codes and is capable
of yielding an alternative construction of the currently best known binary
subspace code of packet length 7, constant dimension 3 and minimum subspace
distance 4.
