Another Product Construction for Large Sets of Resolvable Directed Triple Systems

More large sets of resolvable MTS and resolvable DTS with odd orders

In this paper, we first give a method to construct large sets of resolvableMendelsohn triple systems of order q+2, where q=6t+1 is a prime power. Then, using a computer, we find solutions for t ∈ T ={35, 38, 46, 47, 48, 51, 56, 60}. Furthermore, by amethodwe introduced, large sets of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction ...

An improved product construction for large sets of Kirkman triple systems

It has been shown by Lei, in his recent paper, that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS(v) is a transitive Kirkman triple system of order v, and an LR(u) is a new kind of design introduced by Lei. In this paper, we improve this product construction by removing the condition “there exists a TKTS...

Recursive constructions for large sets of resolvable hybrid triple systems

Complete Sets of Disjoint Difference Families and their Applications

Let G be an abelian group. A collection of (G, k, λ) disjoint difference families, {F0,F1, · · · ,Fs−1}, is a complete set of disjoint difference families if ∪0≤i≤s−1∪B∈FiB form a partition of G− {0}. In this paper, several construction methods are provided for complete sets of disjoint difference families. Applications to one-factorizations of complete graphs and to cyclically resolvable cycli...

A generalisation of t-designs

This paper defines a class of designs which generalise t-designs, resolvable designs, and orthogonal arrays. For the parameters t = 2, k = 3 and λ = 1, the designs in the class consist of Steiner triple systems, Latin squares, and 1-factorisations of complete graphs. For other values of t and k, we obtain t-designs, Kirkman systems, large sets of Steiner triple systems, sets of mutually orthogo...