A conjecture concerning the existence of certain combinatorial designs

This note presents a conjecture about the existence of a particular class of combinatorial designs; the consideration of this particular class of designs was suggested during the course of previous work on modular Hadamard matrices. It is hoped that work on the conjecture will lead to effective general techniques to study incidence matrices whose main features are: they have more columns than rows, and each pair of distinct rows has the same inner product.