ferrite core transformer

It depends on the material the core is made from and how much losses you can stand. Frequencies over 10MHz are often sent through ferrite materials.

What material eg: 3F3 is the core made from.

Working in the UPS field? I rather doubt it.

The manufacturers have very specific data on each core material and what frequency it covers, permeability, hysteresis curves, temperature range, etc..

Ferrite is a generic description and covers a wide range of materials from something suitable for low pass power line filters to coupling/mixing into the microwave ranges.

Look in the catalogs. You can get ferrite cores for much higher frequencies than the ones you're using. The usual limitations on power supply efficiency vs. frequency is parasitic capacitance and diode lag effects, which don't come from the core. This capacitance makes it harder to drive the FETs quickly, and the recovery times of the diodes (should you use them) causes some lost energy each cycle. Dealing with gate capacitance increases circuit complexity, as does eliminating the diodes by using synchronous rectification.

Driving the frequency up is attractive because the core size goes up roughly with the amount of energy it has to store, and the amount of energy stored is roughly proportional to the power supply's power output times one cycle time. This means that a higher switching frequency means smaller cores.

Max "frequency" is very dependent on the core material, as the loss of the core varies widly on type and material. Next is the current and how the winding is done (litz, multifilar, strip, etc). And last, is how fast one can switch the current (actual turn on and turn ooff times. If one gets "fast" enough, then one should think RF "linear" circuits; say class "C" driven ferrite transformers, where one tends to see sine waves for drive and output, with complex conjugate drive at the FET gates.