The zero-sum 5-flow conjecture for non-symmetric designs

A $t$-$(v,k,\lambda)$ design $\mathcal{D}=(X,\mathcal{B})$ consists of a $v$-element point set $X$ and a collection of $k$-subsets of $X$, called blocks, such that every $t$-subset of $X$ lies in exactly $\lambda$ blocks. The design is non-symmetric when its number of blocks differs from its number of points. A zero-sum $n$-flow of $\mathcal{D}$ is a map

$$f:\mathcal{B}\longrightarrow \{\pm1,\ldots,\pm(n-1)\}$$

such that the sum of the values over all blocks incident with each point is zero. The zero-sum 5-flow conjecture. Every non-symmetric design admits a zero-sum $5$-flow. The conjecture was presented in the source as one of two conjectures appearing in earlier work; no resolution is supplied here.