A doubly divisible nearly Kirkman system

In this note we exhibit an example of a new class of combinatorial array. A Room square 9] is an r × r square each of whose cells is either empty or contains a distinct unordered pair with entries from the set of integers {1, 2,…, r + 1} such that each integer appears exactly once in each row and exactly once in each column. We present an analogous square whose entries are unordered triples, none of whose two-element subsets is repeated.