I think it makes a nicer problem to include the case i=j For m <= n then the answer is 2 For m from n+1 to 2n you can get the answer 3 by taking a coordinate frame +- e_i, i = 1..n For larger m there are some bounds in the work of Delsarte, Goethals and Seidel that are relevant. See P. Delsarte, J. M. Goethals and J. J. Seidel, Bounds for systems of lines, and Jacobi polynomials, {\em Philips Research Reports}, {\bf 30} (1975), 91--105. Neil