  Cretan matrices are orthogonal matrices with elements $\leq 1$. These may
have application in forming some new materials. There is a search for Cretan
matrices, especially with high determinant, for all orders. These have been
found by both mathematical and computational methods.
  This paper highlights the differences between theoretical and computational
solutions to finding Cretan matrices.
  It has been shown that the incidence matrix of a symmetric balanced
incomplete block design can be used to form Cretan($v;2$) matrices. We give
families of Cretan matrices constructed using Hadamard related difference sets.
