  We show that in a complex d-dimensional vector space, one can find O(d) bases
whose elements form a 2-design. Such vector sets generalize the notion of a
maximal collection of mutually unbiased bases (MUBs). MUBs have manifold
applications in quantum information theory (e.g. in state tomography, cloning,
or cryptography) -- however it is suspected that maximal sets exist only in
prime-power dimensions. Our construction offers an efficient alternative for
general dimensions. The findings are based on a framework recently established
in [A. Roy and A. Scott, J. Math. Phys. 48, 072110 (2007)], which reduces the
construction of such bases to the combinatorial problem of finding certain
highly nonlinear functions between abelian groups.
