On the construction of balanced repeated measurements designs with good circular properties

Several fields, such as biological, medical, public health, agricultural sciences, etc., require circular balanced repeated measurement designs with fewer unequal number of repeated measurements than the number of treatments. Also, the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units. However, balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case. In this paper, several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed. The proposed construction of designs has high efficiency and, therefore, can save the cost of experimentations due to a fewer experimental subjects. Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters. A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.