https://docs.mongodb.com/manual/reference/ulimit/#linux-distributions-using-systemd documents the limits that should be set on mongod processes. Most of them are (I believe) the default and therefore don't need to be set explicitly, but the default maximum number of open files is 1024, which is much lower than mongodb needs. The /lib/systemd/system/mongodb.service should specify LimitNOFILE=64000 in the Service section.
ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: mongodb-server 1:2.6.10-0ubuntu1
ProcVersionSignature: Ubuntu 4.4.0-38.57-generic 4.4.19
Uname: Linux 4.4.0-38-generic x86_64
NonfreeKernelModules: nvidia_uvm nvidia_modeset nvidia
ApportVersion: 2.20.1-0ubuntu2.1
Architecture: amd64
CurrentDesktop: Unity
Date: Mon Oct 3 10:07:59 2016
InstallationDate: Installed on 2016-01-16 (261 days ago)
InstallationMedia: Ubuntu 15.10 "Wily Werewolf" - Release amd64 (20151021)
SourcePackage: mongodb
UpgradeStatus: Upgraded to xenial on 2016-04-28 (158 days ago)
Some background at: https:/
Presumably mongodb can handle a higher limit securely given that they have documented it, so we should be able to change it.