In the BAMI book, under the section *Capacity of SDRs and the Probability of Mismatches*, it’s written

With typical values such as n = 2048 and w = 40

It isn’t the first time that I see these two numbers as suggestions of typical values for these parameters of an SDR. Is there some theoretical or practical/empirical reason behind this choice of typical values? If yes, what is it? (If not, don’t you think that it is a little bit unscientific to suggest “typical” values that have no “scientific” or “experimental” support?)

In that same section, it is stated that SDRs have a smaller capacity than a dense representation, but, for all practical purposes, if the choice of n and w is sensible, then we can use SDRs to represent an astronomically large number of different objects. Is this the only reason why people say that n = 2048 and w = 40 are the typical values?

In later sections, topics such as “inexact matching” and “subsampling” are described in the context of SDRs. Apparently from the specific mentioned examples, these numbers n = 2048 and w = 40 are, at least in terms of false positives (i.e. matches of two SDRs that are considered equal but are not), (more or less) “appropriate” when using “inexact matching” and “subsampling”, as the probability of false positives with n = 2048 and w = 40 is relatively low.