Tables of Parameters of BIBDs with r⩽41 including Existence, Enumeration, and Resolvability Results

Publisher A balanced incomplete block design (BIBD) is a pair (V,B) where V is a ν set and B is a collection of b k-subsets of V called “blocks” such that each element of V is contained in exactly r blocks, and any 2-subset of V is contained in exactly X blocks. The numbers ν, b, r, k, λ are parameters of the BIBD. A BIBD (V,B) is resolvable if there exists a partition R of its set of blocks B into subsets called “parallel classes,” each of which in turn partitions the set V; R is called a “resolution.” Given a symmetric BIBD (one with u = b , r = k ) , the residual design by deleting all elements of one block and the derived design by deleting all elements of the complement of one block can be obtained.