  A perfect cuboid is a rectangular parallelepiped whose edges, whose face
diagonals, and whose space diagonal are of integer lengths. The problem of
finding such cuboids or proving their non-existence is not solved thus far. The
second cuboid conjecture specifies a subclass of perfect cuboids described by
one Diophantine equation of tenth degree and claims their non-existence within
this subclass. Regardless of proving or disproving this conjecture in the
present paper the Diophantine equation associated with it is studied and is
used in order to build an optimized strategy of computer-assisted search for
perfect cuboids within the subclass covered by the second cuboid conjecture.
