This paper reports the construction of a tetramagic square of order 48.Traditionally, multimagic squares have been constructed primarily via algebraic methods,such as the Tarry-Cazalas method; the previous minimum order was 243.This study achieves order 48 by reducing the construction to a vector subset sum problem and solving it via a cascaded meet-in-the-middle approach.The search space was effectively narrowed by restricting the configuration to a symmetrical arrangement.This result updates the known upper bound for the minimum order of tetramagic squares. Included files:TetramagicSquare.pdf : ManuscriptTetramagicSquare.tex : TeX sourceTetramagicSquare48, TetramagicSquare52, etc.: Resulting magic squares Repository:https://github.com/TokusiN/MagicSquaresCollectionIn addition to this Tetramagic Square, it also includes other results and checker code..
Toshihiro Shirakawa (Sat,) studied this question.