Apex domains cannot have CNAME records.
Question and response
Question
dig amnic.net. NS
Answer
amnic.net. 5 NS ns-cdn.amnic.net.
amnic.net. 5 NS ns-pch.amnic.net.
amnic.net. 5 NS ns-pri.amnic.net.
Authority
The response has no authority records.
Additional
ns-cdn.amnic.net. 5 A 194.0.1.26
ns-pch.amnic.net. 5 A 204.61.216.96
ns-pri.amnic.net. 5 A 195.43.75.53
ns-cdn.amnic.net. 5 AAAA 2001:678:4:0:0:0:0:1a
ns-pch.amnic.net. 5 AAAA 2001:500:14:6096:ad:0:0:1
ns-pri.amnic.net. 5 AAAA 2001:7f9:8:53:0:0:0:1
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0