Two uniformity experiments were conducted at the Agricultural Research Station of Sids. Beiny Suei Governorate to study the interrelations among different sizes of squares. samples. and plots during 2004/2005 and 2005/2006 seasons. The trails were transplanted by onion variety Giza 20 and the actual area of each trial was divided into 12 strips. Each strip consisted of 144 ridges considering the ridge as basic unit with total ridges of 1728 and basic units (rows) were separately harvested. Study of interrelations among sizes of squares. samples and plots based on high relative efficiency (high precision). critical limit of coefficient of variation (C.V s 15%) and critical limit of significance (s 5%) between plot means (treatment means) in the two seasons . The relative efficiency (RE) for Latin square design was estimated as related to completely randomized design (CRD) supposing homogeneity of experimental conditions. Results cleared that changing of plot size led to changing square size. changing RE. C.V and consequently critical limit of significance between plot means in the two seasons. The optimum combinations from sizes of squares and plots were 10x10 and 11x11, for 1.8 and 3.6 in2 plot sizes and 9x9 size of square. for 5.4. 7.2 and 9 m2 plot sizes and 8x8 size of square for plot size 10.8 rn and 7x7 size of square for 12.6 and 14.4 m2 plot size and 6x6 size of square for 16.2. 18 and 19.8 m2 plot sizes and 5x5 size of square for 21.6 m2 plot size. Results also recorded the highest gain of precision of Latin square design being 26. 27.61. 33.35. 49.64. 45.64. 93.97. 50.58. 45.24. 3203.24.98. 14.87. and 11.59% in first season and 22.48. 30.20, 26. 33. 29. 11. 25. 49. 26. 42.19 and 27% in the second season with sizes of plots of 1.8. 3.6, 4.5. 7.2, 9. 10.8. 12.6. 14.4. 16.2. 18. 19.3 and 216 m2. respectively. Critical limit of coefficient of variation (C.V s 15%) ranged from 15 to 6.34 % in the first season and from 15 to 10.16 % in the second season. Critical limit of significance between plot means (5 5%) ranged from 0.288 to 0.075 in the first season and from 0.342 to 0.064 in the second season for the optimum combinations. The previous results give researcher a chance to determine his optimum combinations from sizes of squares and plots depending upon variability of his variables. the nature of his treatments and their costs. Also researcher can depend upon maximum gain of precision (RE). critical limit of coefficient of variation (C.V) and critical limit of significance between plot means for indicating homogeneity of the experimental field.