  In this paper, we show that a small minimal blocking set with exponent e in
PG(n,p^t), p prime, spanning a (t/e-1)-dimensional space, is an F_p^e-linear
set, provided that p>5(t/e)-11. As a corollary, we get that all small minimal
blocking sets in PG(n,p^t), p prime, p>5t-11, spanning a (t-1)-dimensional
space, are F_p-linear, hence confirming the linearity conjecture for blocking
sets in this particular case.
