Lower bound on the size of the largest metrically regular subset of the Boolean cube

Strongly metrically regular subsets of the Boolean cube are studied. Iterative constructions of strongly metrically regular sets are presented. Formula for calculating the number of sets obtainable using these constructions is given. Special families of strongly regular sets are constructed and sizes of sets from these families are calculated. Obtained values give us lower bound on the size of the largest metrically regular subset of the Boolean cube with fixed covering radius.