Updating the Incomplete MOLS Table for v up to 100

Incomplete transversal designs have wide application in the construction of other designs such as transversal designs, block designs, frames, statistical designs, and Latin rectangles. Other areas where they are used include telecommunications and network codes, obtaining physically unclonable functions, frequency hopping sequences and powerline communications, and in the construction of certain types of error correcting codes, in particular low‐density‐parity‐check (LDPC) codes and erasure codes. In a table of parameter sets for which and an incomplete TD (ITD or TD TD) is known is given. However, when , there has been no comprehensive review of where one can find a construction for these ITDs. In this aarticle, we do this for in all but a small number of cases. We also provide over a hundred new ITDs.