Cyclic Loop Designs

Abstract

We give cyclic constructions for loop designs with block size $k=3,4,\text{ and }5$, and all values of $v$, and we thereby determine the $(v,\lambda )$ spectrum for LDs with these block sizes. For $k=3,5$ the $(v,\lambda )$ spectrum for LDs is the same as that for cyclic LDs, but this is not true for $k=4$.