Embedding an Incomplete Diagonal Latin Square in a Complete Diagonal Latin Square

A diagonal Latin square of order n can be embedded in a diagonal Latin square of order t if and only if t ⩾ 2 n + 1. An incomplete diagonal Latin square of order n can be embedded in a diagonal Latin square of order, t , if t = 4 n + 4 k , k = 0, 1, 2,..., or t ⩾ 8 n .