# How to deciding on the number of experimental runs in R for orthogonal fractional factorial design?

Presently I am working on designing a questionnaire for my discrete choice experiment. I want to generate an orthogonal fractional factorial design for the following problem-

The respondent has to choose one out of 4 objects (X1, X2, X3, X4). Each of the 4 objects are classified by 10 different attributes. However, the levels are not the same under each of the objects. The table below displays the situation.

The last row denotes the 4 objects.

Now I want to generate the choice sets for my questionnaire. I would like to use orthogonal fractional factorial design. I kept the row with X in order to sort out the redundant combinations from the choice sets.

I have the following questions- 1. How to decide on the number of runs that one has to chose for fractional factorial design? I used AlgDesign to generate the full factorial which consists of 0.768 million combinations. So, I need a modest number of runs, but how much should I target? I do not see any document where one explains how to choose the number of trials/experimental runs. The papers I am following only tell that they have used N number of runs instead of the full factorial.

1. Out of 0.768 million combinations in the full factorial, there will be many which are redundant. For example- I don't want those rows where (X=X1) and A=(2 or 3 or 4 or 5). There are many other such cases which I don't want in my design. I have coded all levels for each attribute and that's why they are in the full factorial. How do I generate an orthogonal fractional factorial so that it does not contain such redundant combinations? I included the X attribute with the purpose of dropping those combinations conditioned upon specific values of X and other factors. Should I execute that and then generate the fractional factorial using optFederov from the remaining data in the dataframe?

I would be highly obliged if you can kindly help me in this regard. I am a student of Economics, so I do not have very deep understanding of the statistical procedure of such algorithms. So, my question might sound extremely naive for which I am sorry.