The dielectric and other properties of a series of low-density polyimide block copolymer aerogels have been characterized. Two different anhydride-capped polyimide oligomers were synthesized: one from 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane dianhydride (6FDA) and 4,4'-oxidianiline (ODA) and the other from biphenyl-3,3',4,4'-tetracarboxylic dianhydride and ODA. The oligomers were combined with 1,3,5-triaminophenoxybenzene to form a block copolymer networked structure that gelled in under 1 h. The polyimide gels were supercritically dried to give aerogels with relative dielectric constants as low as 1.08. Increasing the amount of 6FDA blocks by up to 50% of the total dianhydride decreased the density of the aerogels, presumably by increasing the free volume and also by decreasing the amount of shrinkage seen upon processing, resulting in a concomitant decrease in the dielectric properties. In this study, we have also altered the density independent of fluorine substitution by changing the polymer concentration in the gelation reactions and showed that the change in dielectric due to density is the same with and without fluorine substitution. The aerogels with the lowest dielectric properties and lowest densities still had compressive moduli of 4-8 MPa (40 times higher than silica aerogels at the same density), making them suitable as low dielectric substrates for lightweight antennas for aeronautic and space applications.