Equivalence classes of multiplicative central (pn, pn, pn, 1)-relative difference sets

We show by explicit construction that the equivalence classes of multiplicative central (pn, pn, pn, 1)-RDSs relative to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb Z}_p^n$\end{document} in groups E with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E/{\mathbb Z}_p^n \cong {\mathbb Z}_p^n$\end{document} are in one-to-one correspondence with the strong isotopism classes of presemifields of order pn. We also show there are 1,446 equivalence classes of central (16, 16, 16, 1)-RDS relative to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb Z}_2^4$\end{document}, in groups E for which \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E/{\mathbb Z}_2^4 \cong {\mathbb Z}_2^4$\end{document}. Only one is abelian.