This paper proves impossibility results on achievable parameters 8adce2b778d6f07807cbf876" title="Click to view the MathML source">(α,β) in the regime of e83aa" title="Click to view the MathML source">n,k→∞ with a fixed ratio 802b2eebcab5acb8d66b8463482d050">. 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 af5350e1e92ca3f73ff7f3605" title="Click to view the MathML source">β>1/2 and 963e5721e6cb3320db4d3f02af"> – integer, the 963e5721e6cb3320db4d3f02af">-fold repetition map achieving ad4df2ffb" title="Click to view the MathML source">α=β is asymptotically optimal.
Finally, constraints on configurations of points and hyperplanes in projective spaces over F2 are derived.