Triple arrays and related designs

We consider a problem posed by Donald Preece more than 30 years ago. Let SS be a set of 35 distinct elements. Construct a 7×15 rectangular array AA, each of whose entries is a member of SS, with no symbol repeated in any row or column, with the following properties: (P1)each symbol occurs precisely three times in the array;(P2)any two distinct rows contain precisely five common symbols;(P3)any two distinct columns contain precisely one common symbol;(P4)any row and any column contain precisely three common symbols. We shall present a solution, survey related work, and look toward further problems.