The electric field strength of dielectrics is a function of material thickness, with thinner materials generally exhibiting a higher field strength. Thus, a thinner dielectric has a higher breakdown field.
A common rule o' thumb is that to double the voltage breakdown of a given sheet of insulator, one needs to multiply the thickness by a factor of 4. The exact exponent used depends on the material type, quality, etc, but the gist of it is that thinner materials can have much higher breakdown strength than one would expect from testing a thicker material.
Many other factors play an important role, such as field strength enhancement due to small radii, voltage rate of change, material defects, humidity, temperature, and so forth.
Finally, there is evidence to suggest that certain concentrations of nanoparticle fillers may increase dielectric strength.
Disclaimer: IANAMS (I am not a material scientist), but I have done some high-voltage design. Dielectrics are still a black art, if you ask me. If you don't believe me, ask a dielectrics expert a quantitative question sometime, and see how long the answer is.