Non-Extendible Latin Cuboids

We show that for all integers m ≥ 4 there exists a 2m×2m×m latin cuboid that cannot be completed to a 2m×2m×2m latin cube. We also show that for all even m not in {2,6} there exists a (2m-1)×(2m-1)×(m-1) latin cuboid that cannot be extended to any (2m-1)×(2m-1)×m latin cuboid.

Click here to download the whole paper.