Here are two ways to do it. First, specify that you have 5 factors a-e and you want a resolution 5 design. Resolution 5 means you can estimate pairwise interactions as long as you are willing to assume the effects of three-way interactions are zero. This attempts to find the smallest design that meets these criteria.
>> fracfactgen('a b c d e', [], 5)
ans =
'a'
'b'
'c'
'd'
'abcd'
Alternatively you could request the specific model terms:
>> fracfactgen('a b c d e ab ac ad ae bc bd be cd ce de')
ans =
'a'
'b'
'c'
'd'
'abcd'
These "generators" define how the final design is created. In this case the first four factors a-d are generated in a full factorial fashion, so the entire design has 2^4=16 rows. The fifth factor is generated by multiplying together the other four, e=abcd.
>> fracfact(ans)
ans =
-1 -1 -1 -1 1
-1 -1 -1 1 -1
-1 -1 1 -1 -1
-1 -1 1 1 1
-1 1 -1 -1 -1
-1 1 -1 1 1
-1 1 1 -1 1
-1 1 1 1 -1
1 -1 -1 -1 -1
1 -1 -1 1 1
1 -1 1 -1 1
1 -1 1 1 -1
1 1 -1 -1 1
1 1 -1 1 -1
1 1 1 -1 -1
1 1 1 1 1
This design is only half as big as the 2^5=32 row full factorial, but is capable of estimating all of the terms listed as long as the effects of higher-order terms are zero.
