The Steiner ratio of

Let L2kd be the d-dimensional space with 2k-norm. Given a finite set N of points in this space. Find a connected graph G=(V,E) such that N⊆V and the total length of G is minimal. Such a network is called a Steiner minimal tree (SMT). If we connect pairs of given points only, we find a minimum spanning tree (MST). Whereas an MST is easy to find a method to construct an SMT in L2kd needs exponential time for d=2 and is still unknown for d>2. The Steiner ratio m(d,2k) of L2kd is a measure of how good an MST approximates an SMT. We estimate this quantity.