Parallel Class Intersection Matrices of Orthogonal Resolutions

This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, Bulgaria

Parallel class intersection matrices (PCIMs) have been defined and used in [6], [14], [15] for the classification of resolvable designs with several parameter sets. Resolutions which have orthogonal resolutions (RORs) have been classified in [19] for designs with some small parameters. The present paper deals with the additional restrictions that the existence of an orthogonal mate might impose on the PCIMs of a resolution, and with the effect of both PCIMs usage and the methods for RORs construction described in [19] and [20]. It is shown in several examples how consideration of PCIMs can result in constructing only of solutions which can have orthogonal mates, and thus substantially improve the computation time. There are parameters for which PCIMs make the classification of RORs possible, and also cases when PCIMs directly prove the nonexistence of doubly resolvable designs with certain parameters.