The new GDAL 2.1 is now also packaged for Fedora 23 and 24 which is possible due to the tireless efforts of various Fedora packagers.
Repo: https://copr.fedorainfracloud.org/coprs/neteler/GDAL/
Installation Instructions:
su # Fedora 23+24: # install this extra repo dnf copr enable neteler/GDAL # A) in case of update, simply dnf update # B) in case of new installation (gdal-devel is optional) dnf install gdal gdal-python gdal-devel