I was thinking about the limits of flywheel energy storage and wondered about carbon nanotubes. The amount of energy that can be stored per unit mass in a flywheel depends not on tensile strength but on the ratio of tensile strength to density. I can find sources which discuss CNT tensile strength (both actual tensile strength and upper bounds of what might be possible), and I can find sources giving density, but I haven't found one discussing both. Presumably I can't just take the largest value for the first and the least for the second, because the strongest is probably not the least dense.
So how high of a value can carbon nanotubes have for tensile strength/density? I'm primarily interested in the best case (what could be achieved by painstakingly placing atoms in the perfect place) but 'best in the lab' and 'best in production' would be useful too.