We describe a simple method for construction of blocks of projective spaces $PG_{n-1}(n,2)$. The method uses an irreducible polynomial $p$ of degree $n+1$ over $GF(2)$, which is "good" in the sense that the degrees $x^0,x,x^2,\dots,x^{2^{n+1}-2}$, reduced by $p$, are all different non-zero binary polynomials of degree at most $n$. We found "good" polynomials for $n-3$ and $n-4$, which gave the blocks of $PG_2(3, 2)$ and $PG_3(4,2)$.