I am interested in finding out what is known about the following generalization of balanced incomplete block designs (BIBDs):

"What is the maximum size of a collection $B$ of $v$-dimensional *unit* real vectors with the following property: there exists a constant $\lambda$ such that $\forall x,y\in B$: $x\ne y \implies x\cdot y = \lambda$?"

Such a collection can be derived from a BIBD, but I wonder if larger collections exist?