Partition of ordered triples into uniform holey ordered designs

Abstract

AbstractA large set is a partition of all ordered triples of a ‐set into disjoint ordered designs of order . In this paper, we generalize the large set with to the notion of , representing a partition of all ordered triples of a ‐set into disjoint uniform holely ordered designs s. We show that a exists if and only if and , except for . Moreover, we study the existence of a with every member having a kind of resolution. We show that a resolvable exists if and only if , , , with 27 possible exceptions. For almost resolvable s, we prove the asymptotic existence and present a few infinite families.