Mutually orthogonal equitable Latin rectangles

Let a b = n 2 . We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either ⌈ b n ⌉ or ⌊ b n ⌋ times in each row of the matrix and either ⌈ a n ⌉ or ⌊ a n ⌋ times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of k a × b mutually orthogonal equitable Latin rectangles as a k – MOELR  ( a , b ; n ) . When a ≠ 9 , 18 , 36 , or 100 , then we show that the maximum number of k – MOELR  ( a , b ; n ) ≥ 3 for all possible values of ( a , b ) .