In this dissertation we present new results regarding optimality of block designs with limited resources. The dissertation is organized as follows. The first chapter outlines the theory of optimal block design. The second chapter shows new work in optimal minimally connected block designs with spatial correlation structure. The third chapter details the discovery of the optimal incomplete designs with two blocks. The fourth chapter does the same for the optimal binary incomplete designs with three blocks. The fifth chapter summarizes the techniques used and new results found and lists possible future research topics.