A statistician in Seattle, David H. Doehlert (personal
communication, Oct. 5, 1990) asked one of us if we could
construct designs
for a full quadratic response surface depending on k factors, for k
between 3 and 14, in which the number of runs n is minimal
or close to minimal.
The present paper (dealing with points in a sphere) and its sequel
(dealing with points in a cube) describe the designs we found
and the method used. The chief merit of our designs when compared with
classical ones such as fractional factorial designs,
central composite designs (Box and Wilson, 1951), or uniform shell
designs (Doehlert, 1970), lies in the fact that the number
of runs is minimized, an important consideration when runs are
expensive. . . from a paper
by R. H. Hardin and N. J. A. Sloane