Apex domains cannot have CNAME records.
Question and response
Question
dig ARIN.NET. NS
Answer
arin.net. 4 NS ns3.arin.net.
arin.net. 4 NS u.arin.net.
arin.net. 4 NS ns1.arin.net.
arin.net. 4 NS ns2.arin.net.
Authority
The response has no authority records.
Additional
u.arin.net. 4 A 204.61.216.50
ns1.arin.net. 4 A 199.212.0.108
ns2.arin.net. 4 A 199.71.0.108
ns3.arin.net. 4 A 199.5.26.108
u.arin.net. 4 AAAA 2001:500:14:6050:ad:0:0:1
ns1.arin.net. 4 AAAA 2001:500:13:0:0:0:0:108
ns2.arin.net. 4 AAAA 2001:500:31:0:0:0:0:108
ns3.arin.net. 4 AAAA 2001:500:a9:0:0:0:0:108
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0