Two Latin squares of order n are r-orthogonal if, when superimposed,
there are exactly r distinct ordered pairs. The spectrum of all values of r
for Latin squares of order n is known. A Latin square A of order n is
r-self-orthogonal if A and its transpose are r-orthogonal. The spectrum
of all values of r is known for all orders nî€ =14. We develop randomized
algorithms for computing pairs of r-orthogonal Latin squares of order n and
algorithms for computing r-self-orthogonal Latin squares of order n