You might want to run your .NET Core ping tool with superuser rights on Linux

ICMP echo (ping) on .NET Core on Linux may be too slow if the .NET process is not running with superuser rights. On Windows there is an IcmpSendEcho2 function (from IP Helper library) that allows ICMP echo/reply even for non-superusers. On Linux, it requires working with raw sockets, and requires superuser rights. To work around this limitation, the .NET Core uses a trick to implement System.Net.NetworkInformation.Ping that runs the system ping tool (that can access raw sockets due to SUID bit being set), when superuser rights are not available, see here. But, if you're pinging many hosts and do it frequently (like once per 50ms), spawning a process for each operation might become too slow, putting extra load on the machine and skewing the measurement results. To make fast pings on Linux, you should run your process with superuser rights.
Also, take note that .NET Core currently implements the synchronous Ping API as wrappers around asynchronous methods, so there is next to no benefit going with the sync version for performance reasons (as was the case for .NET Framework).