Apex domains cannot have CNAME records.
Question and response
Question
dig service.arpa. NS
Answer
service.arpa. 5 NS blackhole-1.iana.org.
service.arpa. 5 NS blackhole-2.iana.org.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0