A SERIES OF 3-DESIGNS

Abstract

A t-(v, k, λ_t) design on a finite point set S of the cardinality v is a family Σof k-subsets of S such that every t-subset of S is contained in exactly λ_t members of Σ. Here by using the finite affine geometry, we show the existence of a 3-(2^t, 2^d, λ₃) design with λ₃=φ(t-3, d-3, 2) for every t>d_??_2.