An incomplete block design for treatments in blocks of size is resolvable if the blocks can be partitioned into sets containing each treatment exactly once. The sets are called replicates which is denoted by . Thus, resolvable block designs are exactly those for which the blocks may be partitioned into replicates. Using as the number of small blocks per replicate in a resolvable design, and the total number of small blocks, then and .One special type="#_x0000_t75" umber of treatment s. For an affine resolvable design, the number is necessarily , and so and , where is a multiple of is the limitation imposed by affineness relative to all resolvable designs.
