It is known since Beauville (1979) that if the canonical image $\phi(S)$ of a surface of general type $S$ is a surface, then the degree $d$ of the canonical map $\phi$ satisfies $d\leq 36-9q$, where $q$ is the irregularity of $S$. Beauville has constructed families of examples with holomorphic Euler characteristic $\chi$ arbitrarily large for $d\leq 8$, but for $d\geq 9$ only three examples are known: $d=K^2=9, q=0$ (Tan), $d=K^2=12, q=0$ (Rito) and $d=K^2=16, q=0$ (Persson), where $K$ is a canonical divisor of $S$.

In this talk I will describe the construction of an example with $d=K^2=16, q=\chi=2$ (the boundary case for surfaces with $K^2=8\chi, q=2$) and some examples with $d=16, K^2>16, q=0$. If time permits I will also explain the example with $d=12$.