摘要
Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearly orthogonal Latin squares are provided.It is proved that there exist 3 MNOLS（2m） if and only if m ≥3 nd there exist 4 MNOLS（2m） if and only if m ≥4 with some possible exceptions.
Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearly orthogonal Latin squares are provided.It is proved that there exist 3 MNOLS（2m） if and only if m ≥3 nd there exist 4 MNOLS（2m） if and only if m ≥4 with some possible exceptions.
基金
Supported by the National Natural Science Foundations of China(Nos.11071207,11371308,11301457,11501181)
