This data contains exhaustive listings of nonisomorphic racks of vertically indecomposable modular lattices of at most 40 elements. Racks are obtained when all doubly irreducible elements subject to a certain condition are removed from a lattice. The rack lattices are stored in XZ-compressed SageMath-compatible dig6-format. The data is described in more detail in "Simplifying modular lattices by removing doubly irreducible elements" (Jukka Kohonen, 2023). Supplementary SageMath code can be found in BitBucket <https://bitbucket.org/jkohonen/modular-racks/>.

2023