Without some more details your question is mysterious. But if you think that response of your system is linear to each factor then 24 = 16 experiments should suffice. Why just this number? Just use two extreme levels for each factor.
I think so that The Taguchi method is one of the best experimental methodologies used to find the minimum number of experiments to be performed within the permissible limit of factors and levels.
Check out RESPONSE SURFACE METHODS. A beginning introduction can be found in Montgomery Design and Analysis of Experiments available in the z-library for download. This optimizes factorial designs which are very common designs.. Best wishes David Booth
yes, Reza Shahin, alternatively, response surface method (RSM) also economical to demonstrate mean and variance analysis simultaneously, see for instance
https://www.jstor.org/stable/2684183 by @Raymond H. Myers, Andre I. Khuri and Geoffrey Vining and https://www.researchgate.net/project/Robust-Design-in-commercial-vehicle-braking-systems by Stefan KemmlebAlexander Kremer Mark Henss
Article A comprehensive review of Design of experiment (DOE) for wat...
Please refer to the article that my team wrote. This will offer you some perspective on the type of DOE available and some advantages and disadvantage of each context. It really depends on your application.