Monadic Balanced Ternary Designs

Abstract

This paper investigates the existence of monadic balanced ternary designs (BTDs). A monadic BTD is a BTD where each size $K$ block contains one element that appears doubly and $K-2$ elements that appear singly. The authors show that the conditions

1. ${\rho }_1=2{\rho }_2$,
2. $\mathrm{\Lambda }(V-1)=10{\rho }_2$,
3. $\mathrm{\Lambda }\ne 3$,

are sufficient for the existence of monadic BTDs $(V;B;{\rho }_1,{\rho }_2,R;4;\mathrm{\Lambda })$. The authors also give necessary and sufficient conditions for the existence of monadic BTDs where the block size is five and $\mathrm{\Lambda }$ is 3 or 6.