The (2,3)-generation of the finite 8-dimensional orthogonal groups

We construct $(2,3)$-generators for the finite $8$-dimensional orthogonal groups, proving the following results: the groups $Ω_8^+(q)$ and $PΩ_8^+(q)$ are $(2,3)$-generated if and only if $q\geq 4$; the groups $Ω_8^-(q)$ and $PΩ_8^-(q)$ are $(2,3)$-generated for all $q\geq 2$.

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