Equilateral sets in the ${\mathrm{\ell }}_1$ sum of Euclidean spaces

Let $E^n$ denote the (real) $n$-dimensional Euclidean space. It is not known whether an equilateral set in the ${\mathrm{\ell }}_1$ sum of $E^a$ and $E^b$, denoted here as $E^a{\oplus }_1{E}^b$, has maximum size at least $\dim(E^a \oplus_1 E^b) + 1 = a + b + 1$forallpairsof$a$and$b$. We show, via some explicit constructions of equilateral sets, that this holds for all $a⩽27$, as well as some other instances.