The Structure of Optimal Design Algorithms

The practise of theoretical design has not traditionally been one of those areas of applied mathematics where well-posed questions lead directly to well-de ned answers. Instead, combinatorial arrangements are typically rst proposed as designs on more or less obscure and intuitive grounds; various precisely de ned notions of design optimality might be employed, but almost exclusively to con rm that a design is good, rather than to generate the design in the rst place. But fortuitous combinatorial arrangements are not always available: when they are not, classical design theory leaves the practitioner out in the cold.