blocking (statistics)). There, a design in which each element occurs the same total number of times is called equireplicate, which implies a regular design only when the design is also binary. The incidence matrix of a non-binary design lists the number of times each element is repeated in each block. Regular uniform designs (configurations) The simplest type of "balanced" design (t=1) is known as a tactical configuration or 1-design. The corresponding incidence structure in geometry is known simply as a configuration, see Configuration (geometry). Such a design is uniform and regular: each block contains k elements and each element is contained in r blocks. The number of set elements v and the number of blocks b are related by , which is the total number of element occurrences. Every binary matrix with constant row and column sums is the incidence matrix of a regular uniform block design. Also, each configuration has a corresponding biregular bipartite graph known as its incidence or Levi graph. Pairwise balanced uniform designs (2-designs or BIBDs) Given a finite set X (of elements called points) and integers k, r, λ ≥ 1, we define a 2-design (or BIBD, standing for balanced incomplete block design) B to be a family of k-element subsets of X, called blocks, such that any x in X is contained in r blocks, and any pair of distinct points x and y in X is contained in λ blocks. Here, the condition that any x in X is contained in r blocks is redundant, as shown below. Here v (the number of elements of X, called points), b (the number of blocks), k, r, and λ are the parameters of the design. (To avoid degenerate examples, it is also assumed that v > k, so that no block contains all the elements of the set. This is the meaning of "incomplete" in the name of these designs.) In a table: {| class="wikitable" | v || points, number of elements of X |- | b || number of blocks |- | r || number of blocks containing a given point |- | k || number of points in a block |- | λ || number of blocks containing any 2 (or more generally t) distinct points |- |} The design is called a (v, k, λ)-design or a (v, b, r, k, λ)-design. The parameters are not all independent; v, k, and λ