Abstract
This paper deals with new infinite families of small dense sets in desarguesian projective planes $PG(2,q)$. A general construction of dense sets of size about $3q^{2/3}$ is presented. Better results are obtained for specific values of $q$. In several cases, an improvement on the best known upper bound on the size of the smallest dense set in $PG(2,q)$ is obtained.
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