A t-design with parameters (v, k, 2) is an incidence structure consisting of a set of v points and a set of b blocks with the incidence relation that every block is incident with exactly k points, and every t-subset of points is contained in exactly ^ blocks. An automorphism group of a t-design is a group of permutations on points of the design which maps blocks to blocks and preserves the incidence and non-incidence. A t-design is said to be block-transitive if it admits an automorphism group acting transitively on the block set. In this talk, we present a general construction of a block-transitive t-design that preserves a higher-dimensional grid structure as the point set. We also give explicit constructions of examples for grids of dimensions three and four, and ask several open questions.
