We begin the investigation into the relationship between 𝑛 and 𝑘 by examining design connectivity. First, we find that as designs become sparse, random seed designs more often have zero or near zero values of the determinant of the Fisher information matrix, ℱ . These seed designs are unsuitable for optimization due to being weakly connected or disconnected. For a disconnected graph, at least one 𝜆 𝑖 is precisely zero. Alternatively, in a connected graph, 𝜆 𝑖 values and hence Eq. 8 may approach zero and result in a solution that is not accurately invertible .