Can you use your Oscope to view the voltage from the PWM, with a LC circuit on it? What is the ripple?
You may need some other ckt to get a smooth ( 0.06v) or less, ripple. That is a really critical spec.
Even if the arduino PWM could give that much accuracy, you could lose it if you are using a breadboard with non-soldered wires. For that kind of accuracy, solder all wires that you can.
Is your power supply even that accurate? How about your house voltage?
You may need a high precision (high cost) power supply
for that much accuracy.