Large sets of resolvable idempotent Latin squares

An idempotent Latin square of order vv is called resolvable and denoted by RILS(v)(v) if the v(v−1)v(v−1) off-diagonal cells can be resolved into v−1v−1 disjoint transversals. A large set of resolvable idempotent Latin squares of order vv, briefly LRILS(v)(v), is a collection of v−2v−2 RILS(v)(v)s pairwise agreeing on only the main diagonal. In this paper we display some recursive and direct constructions for LRILSs.