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The present work contributes to the determination of\udthe n-th linear polarization constant cn(H) of an n-dimensional\udreal Hilbert space H. We provide some new lower bounds on the\udvalue of supkyk=1 | hx1, yi · · · hxn, yi |, where x1, . . . , xn are unit vectors\udin H. In particular, the results improve an earlier estimate of\udMarcus. However, the intriguing conjecture cn(H) = nn/2 remains\udopen

The linear polarization constant of Rn