2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108038We present a rigorous proof of an interesting boundary effect of deterministic dense coding first observed by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Namely, it is shown that $d^2-1$ cannot be the maximal alphabet size of any isometric deterministic dense coding schemes utilizing $d$-level partial entanglement.3 pages, RevTeX, no figure. Comments, criticisms and suggestions are welcomeQuantum Physicstext