AbstractWe provide an upper bound of the size of an m-irreducible blocking set in a linear space. This upper bound is a generalization of the Bruen–Thas bound in πq and improves it if m>(q2+q-qq)/(qq+1). We prove that in a finite affine plane αq of order q, two blocking sets mutually complementary are both irreducible, if and only if q=4. Moreover, we determine bounds of the size of a set of class [0,n1,…,nl] in πq, ni≡1modd, i=1,…,l, 2⩽d<q
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