Apex domains cannot have CNAME records.
Question and response
Question
dig net.nz. NS
Answer
net.nz. 5 NS ns1.dns.net.nz.
net.nz. 5 NS ns3.dns.net.nz.
net.nz. 5 NS ns4.dns.net.nz.
net.nz. 5 NS ns5.dns.net.nz.
net.nz. 5 NS ns6.dns.net.nz.
net.nz. 5 NS ns7.dns.net.nz.
net.nz. 5 NS ns2.dns.net.nz.
Authority
The response has no authority records.
Additional
ns1.dns.net.nz. 135346 A 202.46.190.130
ns2.dns.net.nz. 135346 A 202.46.187.130
ns3.dns.net.nz. 135346 A 202.46.188.130
ns4.dns.net.nz. 135346 A 202.46.189.130
ns5.dns.net.nz. 135346 A 185.159.197.130
ns6.dns.net.nz. 135346 A 185.159.198.130
ns7.dns.net.nz. 135346 A 194.146.106.54
ns1.dns.net.nz. 135346 AAAA 2001:dce:2000:2:0:0:0:130
ns2.dns.net.nz. 135346 AAAA 2001:dce:7000:2:0:0:0:130
ns3.dns.net.nz. 135346 AAAA 2001:dce:d453:0:0:0:0:53
ns4.dns.net.nz. 135346 AAAA 2001:dce:d454:0:0:0:0:53
ns5.dns.net.nz. 135346 AAAA 2620:10a:80aa:0:0:0:0:130
ns6.dns.net.nz. 135346 AAAA 2620:10a:80ab:0:0:0:0:130
ns7.dns.net.nz. 135346 AAAA 2001:67c:1010:13:0:0:0:53
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0