Apex domains cannot have CNAME records.
Question and response
Question
dig private.asi-inter.net. NS
Answer
private.asi-inter.net. 5 NS ns2.proxxio.net.
private.asi-inter.net. 5 NS ns1.proxxio.net.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0