Critical sets in nets and latin squares

Abstract

The concept of a critical set in a latin square is extended to the more general setting of nets. A lower bound is given for the size of a critical set in a group-based net. In the case of a general net of degree 3 and order n( n⩾5), it is shown that the size of a critical set is bounded below by n+1. In the proof of this result, a special embedding of a latin square of order m into a suitable latin square of order n is established for every n>2 m.