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Synthesizing networks that satisfy multiple requirements, such as high reliability, low diameter, good embeddability, etc., is a difficult problem to which there has been no completely satisfactory solution. We present a simple, yet very effective, approach to this problem. The crux of our approach is a filtration process that takes as input a large set of randomly generated graphs and filters out those that do not meet the specified requirements. Our experimental results show that this approach is both practical and powerful. The use of random regular networks as the raw material for the filtration process was motivated by their surprisingly good performance with regard to almost all properties that characterize a good interconnection network. We provide results related to the generation of networks that have low diameter, high fault tolerance, and good embeddability. Through this, we show that the generated networks are serious competitors to several traditional well-known networks. We also explore how random networks can be used in a packaging hierarchy and comment on the scope of application of these networks.