If your PC is not enough, you should use distributed testing in
Jmeter
Keep in mind, that in theory you can send 4000 requests per second,
they will spend some time on the way to the server, so there is
probability that they will come not in 1 second. To avoid this, try
to use high bandwidth lan( for example, you can host your server in
Azure cloud and install Jmeter in cloud too. )
If you will have no success with JMeter try to use Tank This
tool specialized on high loading, and it should be possible to send
even 10k requests in 1 second from 1 machine.