Found a program to calculate, which gives me around a 8cm sized antenna for 93.8MHz:
That can't be correct. Since the wavelength is about 3 meters in the FM band a quarter wave dipole or groundplane should have elements with a length of about 75 cm.
So for a dipole:
<-75-> <-75->
_______ _______
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That's probably the easiest to do, just hang it vertical and you will not have a directional effect and you will not need a ground plane.
Math is simple.
Speed of light: 299,792,458 meters per second
Frequency: 93,800,000 cycles per second.
so 299,792,458 m/s divided by 93,800,000 cycles/s = X meters per cycle (seconds cancel each other), so 3.1960816417910447761194029850746 m per wavelengh cycle.
quarterwave 0.79902041044776119402985074626866 m or 80 cm (not 8cm)
Edit: 8cm would be for 10 times the frequency so 938MHz, maybe you put one 0 too many