Foundations of Software Testing: Fundamental Algorithms and Techniques

Test Generation

in order. In a Latin square based on letters A, B, ...,theelements in the

top row and the leftmost column are arranged in alphabetical order.

4.5 MUTUALLY ORTHOGONAL LATIN SQUARES

Let M

1

and M

2

be two Latin squares, each of order n. Let M

1

(i, j ) and

M

2

(i, j ) denote, respectively, the elements in the i

th

row and j

th

column

of M

1

and M

2

. We now create an n × n matrix M from M

1

and M

2

such that the L(i, j )isM

1

(i, j )M

2

(i, j ), that is we simply juxtapose the

corresponding elements of M

1

and M

2

. If each element of M is unique,

that is it appears exactly once in M,thenM

1

and M

2

are said to be

MOLS of order n.

Example 4.13: There are no MOLS of order 2. Listed below are two

MOLS of order 3:

M

1

=

123

231

312

M

2

=

231

123

312

To check if indeed M

1

and M

2

are mutuall ...