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 $(n= 1,2,3,\dots)$. The computation is based on the property that every two isotopic $n$-quasigroups are 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.