The points that provide the extremes of the factors are known as the "star points." Suppose the value of the extreme is A. In this case,
A=sqrt(2)
would be appropriate for a design having two factors. For N factors, it is a N-dimensional sphere, rather than a square passing through the corners of the cube. If that were the only consideration, we would use
A=sqrt(N)
In fact, though, there is a criterion known as "rotatability" that dictates we should set A=N^(1/4), where N is the number of points in the cube portion of the design.
For 14 factors, a full factorial would have 2^14 points in the cube. The CCDESIGN function instead uses a half fraction of the full factorial, so N is half of this value, and A is
star = ((2^14) / 2) ^ (1/4)
To know how many star points are generated for a 14 factor design:
Dc=ccdesign(14,'type','circumscribed');
star=((2^14) / 2) ^ (1/4);
ind =find(abs((Dc(:,:))==star));
"ind" tells you that there are exactly 14 star points.
