Counterexamples to the Woods Conjecture in dimensions d = 24

摘要

Let N-d be the greatest value of covering radius over all well-rounded unimodular d dimensional lattices. In 1972 A. C. Woods conjectured that N-d = 30. In this paper we give counterexamples to the Woods conjecture in dimensions d >= 24. Then the unknown dimensions of the Woods conjecture are 14 dimensions 10 <= d <= 23.