The BWF law specifies the feather count
Badminton World Federation
Law 2.2.1 in Version 5.0 (2) specifies 16 feathers fixed into the base of a feathered shuttle.
Based on: Badminton World Federation

Yes. BWF's Laws of Badminton, Version 5.0 (2), in force from 26 April 2025, specify 16 feathers fixed into the base of a standard feathered shuttlecock.
The requirement appears in Law 2.2.1. Independent research published in the New Journal of Physics also describes a feathered shuttlecock built with 16 feathers, corroborating the standard construction.
The qualifier 'feathered' matters. The laws separately cover non-feathered shuttles, whose synthetic skirt replaces natural feathers. The count is also only one specification: dimensions, weight and other requirements remain relevant.
Sixteen feathers is the standard specified for feathered shuttlecocks; synthetic skirts are covered by separate provisions.
Badminton World Federation
Law 2.2.1 in Version 5.0 (2) specifies 16 feathers fixed into the base of a feathered shuttle.
Based on: Badminton World Federation
Cohen, Darbois Texier, Quéré and Clanet
The researchers describe a feathered shuttlecock with 16 feathers set into a cork base. This corroborates the construction, while the BWF document establishes the rule.
Based on: New Journal of Physics
Badminton World Federation
Law 2.3 covers non-feathered shuttles, replacing natural feathers with a synthetic skirt or simulation. The 16-feather specification should not be generalized to every shuttle.
Based on: Badminton World Federation
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