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How to plot points of size less than 1?

I have a huge sequence L (say of length $n=10^6$) and I would like to plot all the points (i,L[i]) for i in range(n).
To do so, the following works.

points([(i,L[i]) for i in range(n)],size=1)

The problem is that size=1 (for the points) is too large for a satisfactory plotting.

But if $r$ is a fixed float with $0< r <1$, then

points([(i,L[i]) for i in range(n)],size=r)

is interpreted as

points([(i,L[i]) for i in range(n)],size=0)

which is an empty plotting (so not working).

Question: How to rewrite the second command line above to really plot points of size=r?