A small ultrafilter number at all ${\mathrm{\aleph }}_3\le \kappa <{\mathrm{\aleph }}_{\omega }$

This note shows how recent work of Eskew and Hayut can be combined with a method of Raghavan and Shelah to show the consistency of ${\mathfrak{u}}_{\kappa }<2^{\kappa }$ for ${\mathrm{\aleph }}_3\le \kappa <{\mathrm{\aleph }}_{\omega }$, from a huge cardinal.