Minimum rectilinear Steiner tree of n points in the unit square

Chung and Graham conjectured (in 1981) that n points in the unit square [0,1]2 can be connected by a rectilinear Steiner tree of length at most n+1. Here we confirm this conjecture for small values of n, and for some new infinite sequences of values of n (but not for all n). As an interesting byproduct we obtain close rational approximations of n from below, for those n.