# Are minimum boolean circuit sizes for small problem sizes of an NP-complete problem known?

I think that a table with the following numeric values would be very interesting, but I could not find any table online displaying them:

Choose any NP-complete problem (say, clique, but a problem having well defined instances of $$n$$-bit size for every $$n$$ is probably best for this question). For each value of $$n$$ (input size), there is a minimum size boolean circuit that solves the problem for instances of size $$n$$. It is obviously computationally hard to actually compute these minimum sizes, but they can be computed by exhaustive search for small values of $$n$$.

Is there any table of such values for small $$n$$ known?

• Not a boolean circuit, but interesting nonetheless. The minimal size sorting circuit for $n$ inputs. – orlp Mar 31 '20 at 22:24