Optimal design in irregular BIBD settings

When the necessary conditions for a balanced incomplete block design (BIBD) are satisfied, but no BIBD exists, there is no simple answer for the optimal design problem. In such an irregular BIBD setting, identification of an A-optimal or D-optimal design requires a delicate interplay of combinatorics and optimality tools. Here the known theory is extended, giving a more comprehensive picture of the set of potentially optimal designs and affording a better understanding of the relationship between optimality and simple combinatorial measures of symmetry. The theory in conjunction with an intricate search leads to the A- and D-optimal design for D(15,21,5); this is the first known optimal design for an irregular BIBD setting. Insight is also gained on resolvable members of D(15,21,5).