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We establish two theorems on the embedding of k-cap in an ovaloid of $S_{3,q}(q>2)$. Moreover, we prove that $M_4=q^2-2=14$, where $M_q$ denotes the maximum number of points that can lie in a non-ovaloid complete cap.

We prove that the only $K_{r,q}^3$ non contained in any cap of lower kind are the sets projectively equivalent to $5_{3,2}^3$ and ${11}_{4,3}^3$ constructed in [8] by G. Tallini.