Experience with planar antennas in MWO

With the top boundary as "open = 377 ohms" , what is the minimum height of the top layer required to get correct input impedance. I knew the short commings of the conductor walls of the design space: but I thought if the top boundary is open, it shouldn't matter how thick it is. The thicker the layer, the greater the design area required to keep the calculation space from being a cavity!

The height of top layer should be much more, than lambda (mean for microstrip structure) for boundary effect (with open =377) avoidence