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

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 ...

Resolvable Designs with Large Blocks

Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix, and consequently in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Su...

Product constructions for large sets of resolvable MTSs and DTSs

Recursive constructions for large sets of resolvable hybrid triple systems

Resolvable Group Divisible Designs with Large Groups

We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete mult...