Cyclotomic Conditions Leading to New Steiner 2-Designs

We improve the constructions of S. Bagchi and B. Bagchi for Steiner 2-designs which are point-regular over the additive group of a Galois ring. As a consequence, we get new cyclotomic conditions leading to point-regular Steiner 2-designs with block sizek? {7, 9, 11, 13, 17}.