On solvability of the axial $8$-index assignment problem on one-cycle permutations

We study the axial $8$-index assignment problem on one-cycle permutations. For a long time the question of solvability of its set of constraints for one-cycle permutations of length $n$ in the case of $8$ indices remained open. We prove that the set of constraints have a solution if $n$ is odd and greater than $87$. Ill. 4, bibliogr. 11.