stylistic:tone
Transversal designs

A transversal design with k groups of size n and index λ, denoted T, is a triple (X, G, B) where:

The existence of a T design is equivalent to the existence of k -2 MOLS(n).

A transversal design T is the dual incidence structure of an (k,n)-net. That is, it has nk points and n blocks. Each point is in n blocks; each block contains k points. The points fall into k equivalence classes (groups) of size n so that two points in the same group are not contained in a block while two points in different groups belong to exactly one block.

For example, using the (5,4)-net of the previous section we can construct a T transversal design. The block associated with the point (i, j) of the net will be denoted b. The points of the design will be obtained from the following scheme: r ↔ i, c ↔ 5 j, and l ↔ 5 i + j. The points of the design are thus denoted by the integers 1,..., 20. The blocks of the design are:

The five "groups" are: