Monadic Balanced Ternary Designs

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. \( \Lambda(V-1) = 10\rho_2 \),
3. \( \Lambda \neq 3 \),

are sufficient for the existence of monadic BTDs \( (V; B; \rho_1, \rho_2, R; 4; \Lambda) \). The authors also give necessary and sufficient conditions for the existence of monadic BTDs where the block size is five and \( \Lambda \) is 3 or 6.