A SIMPLE GENERALIZED CONSTRUCTION OF RESOLVABLE BALANCED INCOMPLETE BLOCK DESIGNS WITH PRIME BLOCK SIZES

Abstract

This paper presents a Simple Generalized Construction of Resolvable Balanced Incomplete Block Designs whose parameter combination is of the form $v=k^2, ~r=k+1, ~\lambda=k^0=1$, where $k$ is prime. The design construction was achieved by using the cyclic subgroup of the symmetric group $S_k$ whose generator is one of the permutations of the $2$-permutation generating set of the Dihedral group $D_k$ and $2$-permutation generating set of the presentation of $S_k$. The method is efficient, sufficient and also mitigate against the tediousness encountered in other methods of construction when $v$ is large.