  A {\em pseudo-arc} in $\mathrm{PG}(3n-1,q)$ is a set of $(n-1)$-spaces such
that any three of them span the whole space. A pseudo-arc of size $q^n+1$ is a
{\em pseudo-oval}. If a pseudo-oval $\mathcal{O}$ is obtained by applying field
reduction to a conic in $\mathrm{PG}(2,q^n)$, then $\mathcal{O}$ is called a
{\em pseudo-conic}.
  We first explain the connection of (pseudo-)arcs with Laguerre planes,
orthogonal arrays and generalised quadrangles. In particular, we prove that the
Ahrens-Szekeres GQ is obtained from a $q$-arc in $\mathrm{PG}(2,q)$ and we
extend this construction to that of a GQ of order $(q^n-1,q^n+1)$ from a
pseudo-arc of $\mathrm{PG}(3n-1,q)$ of size $q^n$.
  The main theorem of this paper shows that if $\mathcal{K}$ is a pseudo-arc in
$\mathrm{PG}(3n-1,q)$, $q$ odd, of size larger than the size of the second
largest complete arc in $\mathrm{PG}(2,q^n)$, where for one element $K_i$ of
$\mathcal{K}$, the partial spread
$\mathcal{S}=\{K_1,\ldots,K_{i-1},K_{i+1},\ldots,K_{s}\}/K_i$ extends to a
Desarguesian spread of $\mathrm{PG}(2n-1,q)$, then $\mathcal{K}$ is contained
in a pseudo-conic. The main result of \cite{Casse} also follows from this
theorem.
