Abstract
G. Gratzer, H. Lakser, and E. T. Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a “small” lattice L, that is, a lattice L with O(n 2 ) elements. G. Gratzer, I. Rival, and N. Zaguia proved that, for any α<2, O(n 2 ) can not be improved to O(n α ). In this note we show that the theorem about small representation can be improved further to get a more delicate result.
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