  The first published non-trivial examples of algebraic surfaces of general
type with maximal Picard number are due to Persson, who constructed surfaces
with maximal Picard number on the Noether line $K^2=2\chi-6$ for every
admissible pair $(K^2,\chi)$ such that $\chi \not\equiv 0 \text{ mod } 6$. In
this note, given a non-negative integer $k$, algebraic surfaces of general type
with maximal Picard number lying on the line $K^2=2\chi-6+k$ are constructed
for every admissible pair $(K^2,\chi)$ such that $\chi\geq 2k+10$. These
constructions, obtained as bidouble covers of rational surfaces, not only allow
to fill in Persson's gap on the Noether line, but they provide infinitely many
new examples of algebraic surfaces of general type with maximal Picard number
above the Noether line.
