Let $\mathcal{C}/K$ be a smooth plane curve of degree $d$, and $p:=char(K)\geq 0$. If $p\nmid (d-1)$, it is well-known that $\mathcal{C}$ has $3d(d-2)$ inflection points (counted with multiplicity). Without taking multiplicity into account, Fermat curves $$x^d+y^d+z^d=0,$$
have exactly $3d$ inflection points (the ones with $xyz=0$), provided that $p\nmid (d-1)$.
Question: Ignoring multiplicities: Are there smooth curves of degree $d$ with less then $3d$ inflection points? Any example? (perhaps in positive characterisitcs?)