Resolvable Designs With Unequal Block Sizes

Resolvable block designs for v varieties in blocks of size k require v to be a multiple of k so that all blocks are of the same size. If a factorization of v is not possible then a resolvable design with blocks of unequal size is necessary. Patterson & Williams (1976) suggested the use of designs derived from α -designs and conjectured that such designs are likely to be very efficient in the class of resolvable designs with block sizes k and k – 1. This paper examines these derived designs and compares them with designs generated directly using an interchange algorithm. It concludes that the derived designs should be used when v is large, but that for small v they can be relatively inefficient.