Designs Having the Parameters of $P{G}_{i+1}(d+1,q)$

Abstract

A construction is given which uses ${\text{PG}}_i(d,q)$ and $q$ copies of ${\text{AG}}_i(d,q)$ to construct designs having the parameters of ${\text{PG}}_{i+1}(d+1,q)$, where $q$ is a prime power and $i\le d-1$.