Non-Ramanujancy of Euclidean graphs of order 2r

Graphs are attached to the n-dimensional space Z"2"^"r^n where Z"2"^"r is the ring with 2^r elements using an analogue of Euclidean distance. The graphs are shown to be non-Ramanujan for r=4. Comparisons are made with Euclidean graphs attached to Z"p"^"r^n for p an odd prime. The percentage of non-zero eigenvalues of the adjacency operator attached to these finite Euclidean graphs is shown to tend to zero as n tends to infinity.