In 1986, Kreher and Radziszowski first used the famous LLL algorithm to construct combinatorial designs. Subsequently, lattice algorithms have been applied to construct a large variety of objects in design theory, coding theory and finite geometry. Unfortunately, the use of lattice algorithms in combinatorial search is still not well established. Recently, a new enumeration strategy based on "limited discrepancy search" was used to further improve the power of this method. In this talk, we will describe the search strategy based on lattice basis reduction, compare it to widely used backtracking algorithms and integer linear programming algorithms, and will outline the recent progress.

https://link.springer.com/chapter/10.1007/978-3-030-79987-8_2