On the existence of k-homogeneous Latin bitrades

Following the earlier work on {homogeneous Latin bitrades by Cavenagh, Donovan, and Dr'apal (2003 and 2004) Bean, Bidkhori, Khosravi, and E. S. Mahmoodian (2005) we prove the following results. All k-homogeneous Latin bitrades of volume km exist, for 1) all odd number k and m is greater than or equal to k, 2) all even number k > 2 and m is greater than or equal to min{k +u,3k/2}, where u is any odd number which divides k, 3) all m is greater than or equal to k, where k is greater than or equal to 3 and is lesser than or equal to 37.