what is the smallest transformer one can use for an inverter circuit.

[Artisticano.black]

Hi guys, I am working on a project where I want to step up a 3.7 volt DC supply from a 500mah lipo Battery into voltages as high as 250V, so essentially I am looking at making an inverter but the key constraint is the size aspect of it. I want to make it as compact as possible. With dimensions of around 15X15X10 mm. I was wondering if I can use an EE10 transformer for the job. Also if you can share the schematics for some sort of inverter or maybe an EMP device that might do the above mentioned task.