Looking on the internet deeply has found these results:

within the scope of is the most popular phrase on the web.

under the scope of 111,000,000 results on the web	within the scope of 1181,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
label scheme while fresh food would be excluded. It has to be made clear that they fall under the scope of this regulation. Activities of operators to indirectly reduce greenhouse gas emissions do not fall under the scope of the Directive. 'Horizontal' BREFs shall include information of a generic nature that can be used across many activities which fall under the scope of Directive 2010/75/EU. It is equally incomprehensible why processed food should fall under the scope of the eco It should therefore be made clear that, even if they are part of e.g. metal lids, gaskets fall under the scope of Directive 2002/72/EC. Estaleiros Navais de Viana do Castelo S.A. builds these ships and consequently the aid to this shipyard falls under the scope of this Regulation. In case of neighbouring authorities in Member States which fall under the scope of the RIS Directive, the data interchange should be done electronically.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

under the scope of

111,000,000 results on the web

within the scope of

1181,000,000 results on the web

More popular!

label scheme while fresh food would be excluded.
It has to be made clear that they fall under the scope of this regulation.
Activities of operators to indirectly reduce greenhouse gas emissions do not fall under the scope of the Directive.
'Horizontal' BREFs shall include information of a generic nature that can be used across many activities which fall under the scope of Directive 2010/75/EU.
It is equally incomprehensible why processed food should fall under the scope of the eco
It should therefore be made clear that, even if they are part of e.g. metal lids, gaskets fall under the scope of Directive 2002/72/EC.
Estaleiros Navais de Viana do Castelo S.A. builds these ships and consequently the aid to this shipyard falls under the scope of this Regulation.
In case of neighbouring authorities in Member States which fall under the scope of the RIS Directive, the data interchange should be done electronically.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.