Department of Mathematics2024-12-2920230925-102210.1007/s10623-023-01314-52-s2.0-85176553796https://doi.org/10.1007/s10623-023-01314-5https://hdl.handle.net/20.500.14288/23539A lower bound is presented for the minimal number of filled cells in a maximal partial Latin hypercube of dimension d and order n. The result generalises and extends previous results for d= 2 (Latin squares) and d= 3 (Latin cubes). Explicit constructions show that this bound is near-optimal for large n> d . For d> n , a connection with Hamming codes shows that this lower bound gives a related upper bound for the same quantity. The results can be interpreted in terms of independent dominating sets in certain graphs, and in terms of codes that have covering radius 1 and minimum distance at least 2.Computer scienceTheoryMethodsMathematicsAppliedJournal article1573-75861103668500002Q241682