  We investigate how Legendre $G$-array pairs are related to several different
perfect binary $G$-array families. In particular we study the relations between
Legendre $G$-array pairs, Sidelnikov-Lempel-Cohn-Eastman
$\mathbb{Z}_{q-1}$-arrays, Yamada-Pott $G$-array pairs,
Ding-Helleseth-Martinsen $\mathbb{Z}_{2}\times \mathbb{Z}_p^{m}$-arrays, Yamada
$\mathbb{Z}_{(q-1)/2}$-arrays, Szekeres $\mathbb{Z}^m_{p}$-array pairs, Paley
$\mathbb{Z}^m_{p}$-array pairs, and Baumert $\mathbb{Z}^{m_1}_{p_1}\times
\mathbb{Z}^{m_2}_{p_2}$-array pairs. Our work also solves one of the two open
problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we
provide several computer search based existence and non-existence results
regarding Legendre $\mathbb{Z}_n$-array pairs. Finally, by using cyclotomic
cosets, we provide a previously unknown Legendre $\mathbb{Z}_{57}$-array pair.
