Generating all nite modular lattices of a given size

Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [6] developed an algorithm to enumerate, up to isomorphism, all nite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. We also show that 2n−3 is a lower bound for the number of nonisomorphic modular lattices of size n.