A construction of OA(st,t+1,s,t) by nonlinear functions and some classification for s=4

In this paper, we treat the case of s⩾4. Firstly, we show a construction theorem of OA(st,t+1,s,t) by utilizing nonlinear functions over GF(s), where s=pl, p a prime, and l a multiple of p. Secondly, we classify OA(4t,t+1,4,t) for t=2, 3 and 4 by utilizing their functional representations.