Before revision:  More generally, there are inherent bounds on the complexity of control networks based solely on transcription factors. I show that given n transcription factor genes in a genome and address combinations of length k then there are at most n/k k-length TF-addresses in the address space.
After revision:  It is proven that given n transcription factor genes in a genome and address combinations of length k then there are at most n/k k-length TF-addresses in the address space.