My textbook said a balanced design with covalency 0 is a complete design.
I don't understand this, because
$$\begin{gather} \text{set of varieties}=\{v_1,v_2,v_3\}\\ B_1 = \{v_1\},\\ B_2 = \{v_2\},\\ B_3 = \{v_3\}\end{gather}$$ is a design that is regular, covalency $0$ for all distinct varieties, and is incomplete.
Why is a balanced design with $0$ complete?
Is your textbook "Introduction to Combinatorics" by Wallis and George, by any chance? If so, it contains the following passage:
"A balanced design with $\lambda = 0$, or a null design, is often called "trivial," and so is a complete design."
In that sentence, they mean "A design is called trivial if either $\lambda = 0$ or it is a complete design." They do not mean "$\lambda = 0$ implies the design is complete."
