Improvement of the Delsarte bound for \(\tau\)-designs when it is not the best bound possible
The problem for obtaining lower bounds on the size of designs in polynomial metric spaces is considered. The authors obtain necessary and sufficient conditions for the existence of improvements (by using linear programming) of the classical Delsarte bound. These conditions are the counterpart to corresponding conditions for codes and the test functions introduced appear to be special cases of the test functions for codes. The conditions are investigated in the general case and for infinite polynomial metric spaces. When improvements of the Delsarte bound are possible, some new bounds are constructed.
scientific article; zbMATH DE number 1902908