To construct a difference matrix with parameters (39,6,1):

 Let A1 = 1    A2=  0   0   0   0   0   0
          16        4  23  13   5  12  11
          22       25  11  22  34  23   6
          17       13   4  20  17  15  29
          38       27  21   8  16  19  26
          23       16  19  34  38  26  21


Define automorphisms T1, T2 by T1(a,b,c,d,e,f) = (16c,16a,16b,16f,16d,16e)
                         T2(a,b,c,d,e,f) = (-a,-b,-c,-d,-e,-f)


Apply the group of order 2 generated by T2 to the column of A1 and the
group order 6 generated by T1, T2 to the columns of A2.  Append a
column of zeros; this gives a (39,6,1) DM.

-- Julian Abel