Is their an efficient mathematical way to estimate the distribution of minimal hamming distances for a set of random strings of length 8 over a 4-letter alphabet? E.g. given a set of 100-10,000 strings of length 8 over a 4-letter alphabet, determine for each sequence the minimal distance from the rest of the set and construct the overall distribution.

The motivation is bioinformatic e.g. comparing the observed vs. expected distributions to learn about the point-mutation rate. The observed distribution is calculated explicitly from the data but it would be nice to estimate the expected distribution mathematically. I assume that any deviation from a random distribution is caused by point mutations.

This is very related to a previous post which spoke about the expected minimal hamming distance but not the distribution itself.

Is their an efficient mathematical way to estimate the distribution of minimal hamming distances for a set of random strings of length 8 over a 4-letter alphabet? E.g. given a set of 100-10,000 strings of length 8 over a 4-letter alphabet, determine for each sequence the minimal distance from the rest of the set and construct the overall distribution.

The motivation is bioinformatic e.g. comparing the observed vs. expected distributions to learn about the point-mutation rate. The observed distribution is calculated explicitly from the data but it would be nice to estimate the expected distribution mathematically. I assume that any deviation from a random distribution is caused by point mutations.

This is very related to a previous post which spoke about the expected minimal hamming distance but not the distribution itself.