Abstract.(1) For any integers n ≥ 1 and g ≥ 2, there is a closed 3-manifold M n g which admits a distance n Heegaard splitting of genus g except that the pair of (g, n) is (2, 1). Furthermore, M n g can be chosen to be hyperbolic except that the pair of (g, n) is (3, 1). (2) For any integers g ≥ 2 and n ≥ 4, there are infinitely many non-homeomorphic closed 3-manifolds admitting distance n Heegaard splittings of genus g.
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