**
Figure 29.
**

As Lunda-designs may be considered as matrices,
it is quite natural to define addition of Lunda-designs
in terms of matrix addition: the sum of two (or more)
matrices (of the same dimensions) is the matrix in which the
elements are obtained by adding corresponding elements
(see the example in Figure 29).

The sum of *k* *m*x*n* Lunda-designs may be called a
*m*x*n Lunda-k-design*. The Lunda-*k*-designs inherit
the following symmetry properties:

(i) The sum of the elements in any row is equal to *km*;
(ii) The sum of the elements in any column is equal to *kn*;
(iii) The sum of the integers in two border unit squares of
any grid point in the first or last rows or columns is equal to *k*;