A000519

[Brendan McKay]

* Brendan McKay <bdm at cs.anu.edu.au> [030419 23:01]:
> * Jim Nastos <nastos at cs.ualberta.ca> [030419 07:03]:
> >   If I'm not mistaken, don't distinct transversal designs map to distinct 
> > latin squares (where the meaning "distinct latin squares" is in the sense 
> > above.) The encyclopedia seems to have no data counting transversal 
> > designs at all.
> 
> I don't see this mapping.  Is it just for particular values of
> k and lambda?  Please expand.

To answer my own question, it is for lambda=1 and k=3. Details
and generalizations in:
  Colbourn, Charles J.(1-VT-C); Dinitz, Jeffrey H.(1-VT-C)
  Mutually orthogonal Latin squares: a brief survey of constructions. 
  Special issue on design combinatorics: in honor of S. S. Shrikhande.
  J. Statist. Plann. Inference 95 (2001), no. 1-2, 9--48.

Brendan.