I am currently in the design phase for an experiment on different packaging attributes and their effects on an actual purchasing choice. In this context, I am asking myself a possibly trivial question: Is the follwing design a true within-design or not?

Each participant chooses one out of 16 products (presented at the same time), which represent the combinations of 4 independent variables (IVs) with two levels each:

 1. size: large or small
 2. shape: bottle or box
 3. material: recycled or not  
 4. brand: sustainable or not

In one sense, it is a 2x2x2x2 factorial design with the resulting 16 conditions/combinations.

I have understood that a within-design means, that **each** participant is tested **under all conditions**. Usually, this is done **sequentially** - in my research, I would present each participant with a choice between large or small, **and then** a choice between bottle or box, **and then**... etc.  However, what if I present the participants with a choice out of **all the 16 combinations at once**? (as described above)  
Is this still a true within-design?

And what does it tell me regarding sample size and analysis tools?  
Do I need 

 - only 30 participants since each makes only one choice (which tells me a combination of the 4 IV they prefer) 
 - or do I need 30x4=120 participants (since I have four IVs) 
 - or do I actually need 30x16=480 participants (because of the 16 conditions/combinations)?

In this sense,  I am also trying to figure out the sample size needed dependent on how many packaging attributes are included as independent variables and whether the experiment is set-up as within or between-subject design.

I have browsed literature on experimental design and power analysis, but haven't come to a clear conclusion yet. Hence, I would be very grateful for some perspective on this.