We　consider　a　general　p-norm　objective　for　experimental　design　problems　that　captures　some　well-studied　objectives　(D/A/E-design)　as　special　cases.　We　prove　that　a　randomized　local　search　approach　provides　a　unified　algorithm　to　solve　this　problem　for　all　nonnegative　integer　p.　This　provides　the　first　approximation　algorithm　for　the　general　p-norm　objective,　and　a　nice　interpolation　of　the　best　known　bounds　of　the　special　cases.　©　2023　Schloss　Dagstuhl-　Leibniz-Zentrum　fur　Informatik　GmbH,　Dagstuhl　Publishing.　All　rights　reserved.