In this paper, we propose a recursive method for constructing intra-resolvable balanced incomplete binary block (B.I.B.) designs. The method leverages the algebraic and geometric structure of finite projective geometries over Galois fields to generate resolvable designs with improved efficiency in terms of block number and treatment repetition. Notably, the recursive construction yields symmetrical and uniform designs suitable for high-dimensional settings. By systematically nesting resolvable blocks, we derive a new class of balanced n-ary designs that are particularly economical and scalable. These designs are of considerable interest to the statistical community due to their broad applicability in resource-constrained experimental environments, such as precision agriculture, high-throughput drug screening, and computer-based simulation studies. Theoretical foundations are supported by explicit constructions and comparative evaluations, demonstrating the advantages of our method over classical approaches.