Since E = h v, a photon of frequency of 10^100 Hz has an energy of 6.626 x 10^66 J. This is clearly an absurd number, and there are no conceivable physical processes which can generate a single photon with so much energy.
Having said that, the two statements you listed are not truly mutually exclusive. It is true that Maxwell's equations do not impose a limit on the frequency of a photon. However, the creation of high-energy photons is constrained by physics in other ways. My understanding is that there must be a change in the energy state of something (e.g. a nucleus, atom, molecule) that corresponds to the energy of the photon.
Yes, Mr. Hsieh, you may be exactly correct. We do not know or do not yet have observed the extraordinary physical process that can generate the photon of frequency of 10^100Hz.
But our current knowledge of the electromagnetism allows at least mathematically the existence of such a ultra, ultra, and ultra high frequency photon. Even 10^1000Hz photon or 10^100000Hz photon or even further higher frequency photon is easy to just write. IF SUCH A HIGH FREQUENCY PHOTON IS IMPOSSIBLE PHYSICALLY IN ACTUAL, THEN WE MUST ASK WHY NOT.
And if so, possibly we might be guided to a discovery of the new physical laws that rule the electromagnetic physics in that extraordinary high frequency range.
My imagination is this. As the temporaly varying speed(frequency) of E, B fields increases very much, the space dimension itself might mix with the time dimension. This dimensional mixing might impede the exsistence of the super ultra high frequency photon. In other words, the space-time might become too viscous for such a photon to exist validly. The medium of the electromagnetism, according to my knowledge is the space itself.