Simple direct constructions for hybrid triple designs

Constructions of simple Mendelsohn designs

A Mendelsohn design M(k,v) is a pair (V,B) t where IV\=v and B is a set of cyclically ordered k-tuples of distinct elements of V, called blocks, such that every ordered pair of distinct elements of V belongs to exactly one block of B. A M( k, v) is called cyclic if it has an automorphism consisting of a single cycle of length v. The spectrum of existence of cyclic M(3,v)'s and M(4,v)'s is known...

Recursive constructions for large sets of resolvable hybrid triple systems

New Constructions for Covering Designs

A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by C(v, k, t). This paper gives three new methods for constructing good coverings: a greedy algorithm similar to Conway and Sloan...

Product constructions for cyclic block designs II. Steiner 2-designs

In [4] we introduced a product construction for cyclic Steiner quadruple systems. The purpose of this paper is to modify the construction so that it is applicable to cyclic Steiner 2-designs. A cyclic Steiner 2-design is a Steiner system s(t, k, u), 2 d t < k < u, in which t = 2 and which has an automorphism of order u. We denote such a system by CS(2, k, u). Under suitable conditions we show h...

Combinatorial constructions for optimal supersaturated designs

Combinatorial designs have long had substantial application in the statistical design of experiments, and in the theory of error-correcting codes. Applications in experimental and theoretical computer science, communications, cryptography and networking have also emerged in recent years. In this paper, we focus on a new application of combinatorial design theory in experimental design theory. E...