I have started with monopole disk antennas but I have very strict size constraints of maximum dimension to be 10 cm. I could get as low as 20 cm only. I use HFSS.
can you make it work from 500MHz and fit into 100mm square? Not sure without trying or modeling. (Thanks to Hagster for pointing that.) If you are getting close try loading it: cut teeth (log periodic tooth antenna, again: idea courtesy of Hagster); sandwitch it between two blocks of plastic.