Large random pattern

I've been trying to create a special random pattern for some time. For example random black dots, like this:

http://ift.tt/2qyFhEI

However, I need a much larger image with about 100,000 points / circles. In principle, no problem, however, the SVG with several MB then becomes too large to open it, for example, with Inkscape, because each circle is drawn individually. Any ideas how this could be realize better resulting in a smaller file. I have already tried something with pattern. Problem is that it should be a truly random, non-repeating pattern.

It's not necessary to do this with dots it could also look like this: [enter image description here][1] http://ift.tt/2r3Wzxa

For ideas / suggestions, I am grateful.

greetings Olli