A Family of Partial Geometric Designs from Three-Class Association Schemes

In this paper, we show that partial geometric designs can be constructed from certain three-class association schemes and ternary linear codes with dual distance three. In particular, we obtain a family of partial geometric designs from the three-class association schemes introduced by Kageyama, Saha, and Das in their article ["Reduction of the number of associate classes of hypercubic association schemes," Ann Inst Statist Math 30 (1978)]. We also give a list of directed strongly regular graphs arising from the partial geometric designs obtained in this paper. (C) 2016 Wiley Periodicals, Inc.