Two-level Cretan Matrices Constructed Theoretically and Computationally using SBIBD

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.