Are there 3 latin squares of order 10 which are pairwise orthogonal?

Are there 7 such latin squares?

We know that there exist pairs of orthogonal latin squares of order 10. Lam's paper proves that there cannot be 9 latin squares any pair of which are orthogonal, and this result can be extended slightly to show that there cannot be 8 pairwise-orthogonal latin squares. Between these results, nothing is known.