Jerrold R. Griggs and Günter Rote:

On the distribution of sums of vectors in general position

In: "Contemporary Trends in Discrete Mathematics." Editors: Ronald L. Graham, Jan Kratochvíl, Jaroslav Nešetřil, and Fred S. Roberts. DIMACS series in discrete mathematics and theoretical computer science, American Mathematical Society, 1999; pp. 139-142.

Abstract

An analog of the Littlewood-Offord problem that was posed by the first author is to find the maximum number of subset sums equal to the same vector over all ways of selecting n vectors in Rd in general position. This note reviews past progress and motivation for this problem, and presents a construction that gives a respectable new lower bound, Omega(2nn1-3d/2), which compares for d>1 to the previously known upper bound O(2nn-1-d/2).
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