Cyclic Loop Designs

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 \( k = 4 \).