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We explore the design parameter space of short (5-25 period), n-doped, Ga/(Al,Ga) As semiconductor superlattices (SSLs) in the sequential resonant tunneling regime. We consider SSLs at cool (77 K) and warm (295 K) temperatures, simulating the electronic response to variations in (a) the number of SSL periods, (b) the contact conductivity, and (c) the strength of disorder (aperiodicities). Our analysis shows that the chaotic dynamical phases exist on a number of sub-manifolds of codimension zero within the design parameter space. This result provides an encouraging guide towards the experimental observation of high-frequency intrinsic dynamical chaos in shorter SSLs. Published by AIP Publishing.