Unital

A Block Design of the form ($q^3+1$, $q+1$, 1).

References

Dinitz, J. H. and Stinson, D. R. ``A Brief Introduction to Design Theory.'' Ch. 1 in Contemporary Design Theory: A Collection of Surveys (Ed. J. H. Dinitz and D. R. Stinson). New York: Wiley, pp. 1-12, 1992.