On the Maximal Number of Columns of a Delta-modular Matrix

We study the maximal number of pairwise distinct columns in a Delta-modular integer matrix with m rows. Recent results by Lee et al. provide an asymptotically tight upper bound of O(m(2)) for fixed Delta. We complement this and obtain an upper bound of the form O(Delta) for fixed m, and with the implied constant depending polynomially on m.