A Cantor set in \(\mathbb R^d\) with ``large'' projections (Q2268632)

\textit{J. Cobb} has raised the question whether for every triple of integers \((d, m, k)\) with \(d>m>k>0\) there is a Cantor set in \(\mathbb{R}^d\) whose projection onto each \(m\) plane has dimension \(k\) [Fundam. Math. 144, No.~2, 119--128 (1994; Zbl 0821.54020)]. The paper's main result answers the question in the affirmative for the case \(k = m-1\).