Latin trades on three or four rows (Q856846)

A Latin trade is the set of entries in which two Latin squares of the same order differ. It is very well known that Latin trades play an essential role in the study of\ critical sets in Latin squares. Let scs\((n)\) be the size of the smallest critical set in any Latin square of order \(n.\) It is a well known and a long-standing conjecture that scs\((n)=\left\lfloor \frac{n^{2}}{4 }\right\rfloor\). The author conjectures that consideration of Latin squares on four rows may establish that scs\((n)\geqslant 2n-4.\) In the paper a conjecture by Cavenagh about such trades is proved for all \(n\leq 9.\)