We show that the Tits index 133 8.1 cannot be obtained by means of the Tits construction over a field with no odd degree extensions. The proof uses a general method coming from the theory of symmetric spaces. We construct two cohomological invariants, in degrees 6 and 8, of the Tits construction and the more symmetric Allison Faulkner construction of Lie algebras of type 8 and show that these invariants can be used to detect the isotropy rank.