Strange flickr on glass during animation

I’m quite new with Blender and this is one of the first animations that I have tried to render:

What I can’t understand is the strange flickr on the base of the glass container.

This is the project file used for the rendering:

Does anyone know what can cause this strange artifacts?

Glass is tough, and you’ve done a good job, so congratulations. These aren’t artifacts, but are refractions of the balls as they bounce. Try increasing the number of “Light Paths” to increase the accuracy of the calculations. I cannot say for sure without rendering the animation, but here is a comparison of one frame (only added 3 seconds on my GPU rendering).

Original (notice the darkness on the rim):

With Full Global Illumination:

You may not need all of these light paths, but pressing this menu and choosing Full Global Illumination is a place to start:

FYI, the number of light paths determines how many bounces a light ray can take. Setting to one, for instance, means the light ray goes out, hits something, and returns a value. Setting to three lets the ray bounce twice before returning a value. Setting to 128 does not mean that it will bounce 128 times (unless you are in a House of Mirrors), just that it can.

Added: more samples may be part of the answer as well.

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Thank you very much Phillip for your quick response!
I will try to render again the scene with the settings updated.