The Design of Gradings with Small Interconnection Numbers for Random Hunt Selectors

An earlier paper [2] presented algorithms for designing gradings for random hunt selectors, The gradings were designed to have a particular kind of combinatorial symmetry called "uniform overlap." The uniform overlap condition is a necessary but not a sufficient condition for grading design. The lack of sufficiency is particularly apparent for gradings With small interconnection numbers. The structural characteristics of such gradings are examined and desirable characteristics of practical gradings are identified. A parameter is defined as a grading characteristic and procedures are presented for designing gradings having minimal values of . Since there is, in general, no unique solution to the problem of designing a uniform overlap grading, the recommendation is made for given reasons that the solution selected should have the smallest value of .