For D = 11 large (uncompactified) spacetime dimensions, the only "string theory" vacuum is M-theory

For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, since type I is S-dual to $Spin(32)/\mathbb{Z}_2$ heterotic?

For D = 4 there is a monstrous number of vacua and there's no full classification

For which values of D a full classification exists, and what is it?

My guess is that the classification exists for $D \geq D_{min}$ but what is the value of $D_{min}$?

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