Concerning the spectrum of perpendicular arrays of triple systems (Q1086568)

A perpendicular array of triple systems of order v is a v(v-1)/6 by 4 array whose rows form a 2-(v,4,2) design and such that the rows of any subarray of 3 columns form a Steiner triple system of order v. Using direct and recursive constructions, it is shown that the necessary condition \(v\equiv 1(mod 6)\) is also sufficient for the existence of perpendicular arrays for \(v\geq 19\) with possible exceptions for \(v=43,55,85,133\).