Voltage spikes are a simple result of Ohm's Law. Current Spike * ESR of Cap.
To improve this impedance ratio consider adding a series ferrite bead and lower ESR cap to ground measured in milliohms from spec.
But 10mV peak is fairly good. If you need much lower then specify or cascade more RLC or RC filtering, but series R affects load regulation by load impedance ratio as well.
First, find where the noise is coming from.
My first thought is that it does not come from a linear regulator.
Could be coming down the mains wiring from who knows what, who knows where.
It look like some of the crud which comes out of the control system for my CNC milling machine.
18 replies and we still do not have a schematic. I think the power supply was purchased and is either welded together or it is cast in concrete so it cannot be opened to see what is inside.