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

A small minimal blocking set in PG(n,p^t), spanning a (t-1)-space, is linear