  In this paper the results of Radloff and Schwabe (2019a) will be extended for
a special class of symmetrical intensity functions. This includes binary
response models with logit and probit link. To evaluate the position and the
weights of the two non-degenerated orbits on the $k$-dimensional ball usually a
system of three equations has to be solved. The symmetry allows to reduce this
system to a single equation. As a further result, the number of support points
can be reduced to the minimal number. These minimally supported designs are
highly efficient. The results can be generalized to arbitrary ellipsoidal
design regions.
