Mutually orthogonal equitable Latin rectangles

Let ab=n2ab=n2. We define an equitable Latin rectangle as an a×ba×b matrix on a set of nn symbols where each symbol appears either ⌈bn⌉ or ⌊bn⌋ times in each row of the matrix and either ⌈an⌉ or ⌊an⌋ times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of kka×ba×b mutually orthogonal equitable Latin rectangles as a k– MOELR (a,b;n)k– MOELR (a,b;n). When a≠9,18,36a≠9,18,36, or 100100, then we show that the maximum number of k– MOELR (a,b;n)≥3k– MOELR (a,b;n)≥3 for all possible values of (a,b)(a,b).