This paper proves impossibility results on achievable parameters (α,β) in the regime of n,k→∞ with a fixed ratio . This is done by developing a general criterion for existence of graph-homomorphism based on the semi-definite relaxation of the independence number of a graph (known as the Schrijver's θ-function). The criterion is then evaluated using some known and some new results from coding theory concerning the θ -function of Hamming graphs. As an example, it is shown that if β>1/2 and – integer, the -fold repetition map achieving α=β is asymptotically optimal.
Finally, constraints on configurations of points and hyperplanes in projective spaces over F2 are derived.