A new method for computing the number of n-quasigroups

We use the isotopy classes of quasigroups for computing the numbers of finite n-quasigroups (n = 1, 2, 3, ...). The computation is based on a property that every two isotopic n-quasigroups are building substructures of the same number of n +1-quasigroups. This is a new method for computing the number of n-quasigroups and in an enough easy way we could compute the numbers of ternary quasigroups of orders up to and including 5 and of quaternary quasigroups of orders up to and including 4.