Recursive Construction of Resolvable Nested Block Designs

This paper proposes a recursive method for constructing intra-resolvable balanced incomplete block designs (BIBDs). The approach exploits the algebraic and geometric structure of finite projective geometries over Galois fields to generate resolvable designs with improved efficiency in terms of the number of blocks and treatment replications. The recursive procedure produces symmetric and uniform designs that are particularly suitable for high-dimensional settings. By systematically nesting resolvable blocks, we derive a new class of balanced n-ary designs that are both economical and scalable. These designs hold significant value for the statistical community, offering broad applicability in resource-constrained experimental environments such as precision agriculture, high-throughput drug screening, and computer-based simulation studies. We provide theoretical foundations through explicit constructions and comparative evaluations, demonstrating the advantages of our method over classical approaches.