I'm trying to compare my work to another work that uses an discrete estimation of Mutual Information. I'll try to keep the example as short as possible.
Let there be a population (n=1000) of solutions, each solution has 3 locations and each location can contain one of 4 symbols. Then the estimated mutual information among the symbols has a certain 'accuracy' as to how close it is to the true mutual information (I don't know what the right term is here). If there were more samples the estimate would improve.
Now I wonder if I don't use 4 symbols but 20 (or any other number) symbols by how much should I increase the population to get a similar accuracy as with just 4 symbols? The symbols come from a random uniform distribution. I'm fairly certain a larger population is needed as the odds of a certain combination of symbols diminishes with the number of possible symbols.