On certain constructions for latin squares with no latin subsquares of order two

AbstractA latin square is said to be an N2-latin square (see[1] and [2]) if it contains no latin subsquare of order 2. The existence of N2-latin squares of all orders except 2k has been proved in [2]. Trivially, there are no such squares of orders 2 and 4. M. McLeish [3] has shown that there exist N2-latin squares of all orders 2k for k ⩾ 6. The present paper introduces a construction for N2-latin squares of all even orders n with n ≠ 0 (mod 3) and n ≠ 3 (mod 5). The problem is thus solved for the orders 24 and 25.For 24, the only remaining case, Eric Regener of the Faculty of Music, Université de Montréal, has constructed the following example of an N2-latin square and kindly granted us the permission to reproduce it here: 81234567823156784314678254682135758273461657182437458213687634512 The existence problem of N2-latin squares is thus completely solved

On a combinatorial problem of antennas in radio astronomy

International audienc