On existence of integral point sets and their diameter bounds

A point set M in m,-dimensional Euclidean space is called an integral point set if all the distances between the elements of M are integers, and M is not situated on an (m-1)-dimensional hyperplane. We improve the linear lower bound for the diameter of planar integral point sets. This improvement takes into account some results related to the Point Packing in a Square problem. Then for arbitrary integers m >= 2, n >= m + 1, d >= 1, we give a construction of an integral point set M of n points in m-dimensional Euclidean space, where M contains points M-1 and M-2 such that the distance between M-1 and M-2 is exactly d.