why there is no pair of orthogonal latin square of order 6?

why there is no pair of orthogonal latin square of order 6? Is there any counter example which shows that these two latin square of order 6 are not orthogonal .

[Rik]

How is this question related to Matlab?

[Ammy]

I think there may be any code in matlab which generate all possible orthogonal latin square . Isn't it ?

[Jan]

Of course you can do it. Simply try it. There are 812'851'200 different Latin square with the side length 6. If you want to compare each of them with all others, you need about 6.6e17 comparisons. If you can compare 1e6 matrices per second, this will take about 20'000 years. I assume, brute force is not an option.

Please explain the background of this question. Is it a homework in a Matlab course or for combinatorics? Where do you take the statement from, that there are no such pairs? Maybe you cannot assume, that all readers are as familiar with the topic as you are. So perhaps you could take the time and define clearly, what "orthogonal Latin squares" are and what exactly a "pair" is - or do you mean pairwise orthogonality?