  A two-dimensional Sp($2N$) vector model with small $\mathcal{N}=4$
superconformal symmetry is formulated, and its chiral algebra is shown to be
generated by superprimary fields of even conformal weight. This vector model is
the large level limit of a coset theory with large $\mathcal{N}=4$, whose
proposed AdS$_3$ dual is a minimal Vasiliev higher spin theory with gauge
algebra generated by fields of even spin. The relation of this vector model to
the symmetric product orbifold, dual to tensionless strings in AdS$_3$ $\times$
S$^3$ $\times$ $\mathbb{T}^4$, is also worked out.
