Blocking varieties in Steiner triples

The problems of Steiner triples blocking applicable in the secret sharing scheme are considered. This paper describes a method for constructing a blocking set of minimum and maximum powers. For the complement blocking set, a method for estimating the minimum complement power in both linear and nonlinear Steiner triples systems is given. For the corresponding matroids, the ideal secret sharing schemes based on interpolation polynomials with zero trace are implemented. For the nonlinear Steiner triples system with 13 elements, the maximum and minimum cardinalities of the complement of the blocking set are found.