Optimal Circular Balanced Repeated Measurements Designs for through the Method of Cyclic Shift (MCS) Rule II

Table 1

Minimal CBRMDs for , using the MCS rule II.

	Set of shifts
5	[1,2,3]t
7	[5,2,3,4,1]t
9	[1,2,3,4,5,6,7]t
11	[1,2,3,6,7,5,4,9,8]t
13	[4,11,2,5,3,10,8,1,6,7,9]t
15	[4,1,6,5,11,10,3,8,9,2,7,12,13]t
17	[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]t
19	[3,4,8,17,5,15,6,7,9,11,10,12,13,16,14,2,1]t
21	[11,8,13,6,15,4,17,2,19,10,1,18,3,16,5,14,7,12,9]t
23	[10,13,8,15,6,17,4,19,2,21,11,1,20,3,18,5,16,7,14,9,12]t
25	[11,14,9,16,7,18,5,20,3,22,1,12,23,2,21,4,19,6,17,8,15,10,13]t
27	[14,11,16,9,18,7,20,5,22,3,24,1,13,25,2,23,4,21,6,19,8,17,10,15,12]t
29	[13,16,11,18,9,20,7,22,5,24,3,26,1,14,27,2,25,4,23,6,21,8,19,10,17,12,15]t
31	[16,13,18,11,20,9,22,7,24,5,26,3,28,1,15,29,2,27,4,25,6,23,8,21,10,19,12,17,14]t
33	[17,14,19,12,21,10,23,8,25,6,27,4,29,2,31,16,1,30,3,28,5,26,7,24,9,22,11,20,13,18,15]t
35	[1,32,3,30,5,28,7,26,9,24,11,22,13,20,15,18,17,16,1,9,14,21,12,23,10,25,8,27,6,29,4,31,2,33]t
37	[19,16,21,14,23,12,25,10,27,8,29,6,31,4,33,2,35,18,1,34,3,32,5,30,7,28,9,26,11,24,13,22,15,20,17]t
39	[18,21,16,23,14,25,12,27,10,29,8,31,6,33,4,35,2,37,19,1,36,3,34,5,32,7,30,9,28,11,26,13,24,15,22,17,20]t
41	[21,18,23,16,25,14,27,12,29,10,31,8,33,6,35,4,37,2,39,20,1,38,3,36,5,34,7,32,9,30,11,28,13,26,15,24,17,22,19]t
43	[20,23,18,25,16,27,14,29,12,31,10,33,8,35,6,37,4,39,2,41,21,1,40,3,38,5,36,7,34,9,32,11,30,13,28,15,26,17,24,19,22]t
45	[23,20,25,18,27,16,29,14,31,12,33,10,35,8,37,6,39,4,41,2,43,22,1,42,3,40,5,38,7,36,9,34,11,32,13,30,15,28,17,26,19,24,21]t
47	[22,25,20,27,18,29,16,31,14,33,12,35,10,37,8,39,6,41,4,43,2,45,23,1,44,3,42,5,40,7,38,9,36,11,34,13,32,15,30,17,28,19,26,21,24]t
49	[25,22,27,20,29,18,31,16,33,14,35,12,37,10,39,8,41,6,43,4,45,2,47,24,1,46,3,44,5,42,7,40,9,38,11,36,13,34,15,32,17,30,19,28,21,26,23]t
51	[24,27,22,29,20,31,18,33,16,35,14,37,12,39,10,41,8,43,6,45,4,47,2,49,25,1,48,3,46,5,44,7,42,9,40,11,38,13,36,15,34,17,32,19,30,21,28,23,26]t
53	[27,24,29,22,31,20,33,18,35,16,37,14,39,12,41,10,43,8,45,6,47,4,49,2,51,26,25,28,23,30,21,32,19,34,17,36,15,38,13,40,11,42,9,44,7,46,5,48,3,50,1]t
55	[28,25,30,23,32,21,34,19,36,17,38,15,40,13,42,11,44,9,46,7,48,5,50,3,52,1,27,26,29,24,31,22,33,20,35,18,37,16,39,14,41,12,43,10,45,8,47,6,49,4,51,2,53]t
57	[29,26,31,24,33,22,35,20,37,18,39,16,41,14,43,12,45,10,47,8,49,6,51,4,53,2,55,28,27,30,25,32,23,34,21,36,19,38,17,40,15,42,13,44,11,46,9,48,7,50,5,52,3,54,1]t
59	[30,27,32,25,34,23,36,21,38,19,40,17,42,15,44,13,46,11,48,9,50,7,52,5,54,3,56,1,29,28,31,26,33,24,35,22,37,20,39,18,41,16,43,14,45,12,47,10,49,8,51,6,53,4,55,2,57]t
61	[31,28,33,26,35,24,37,22,39,20,41,18,43,16,45,14,47,12,49,10,51,8,53,6,55,4,57,2,59,30,29,32,27,34,25,36,23,38,21,40,19,42,17,44,15,46,13,48,11,50,9,52,7,54,5,56,3,58,1]t
63	[32,29,34,27,36,25,38,23,40,21,42,19,44,17,46,15,48,13,50,11,52,9,54,7,56,5,58,3,60,1,31,30,33,28,35,26,37,24,39,22,41,20,43,18,45,16,47,14,49,12,51,10,53,8,55,6,57,4,59,2,61]t
65	[33,30,35,28,37,26,39,24,41,22,43,20,45,18,47,16,49,14,51,12,53,10,55,8,57,6,59,4,61,2,63,32,31,34,29,36,27,38,25,40,23,42,21,44,19,46,17,48,15,50,13,52,11,54,9,56,7,58,5,60,3,62,1]t
67	[34,31,36,29,38,27,40,25,42,23,44,21,46,19,48,17,50,15,52,13,54,11,56,9,58,7,60,5,62,3,64,1,33,32,35,30,37,28,39,26,41,24,43,22,45,20,47,18,49,16,51,14,53,12,55,10,57,8,59,6,61,4,63,2,65]t
69	[35,32,37,30,39,28,41,26,43,24,45,22,47,20,49,18,51,16,53,14,55,12,57,10,59,8,61,6,63,4,65,2,67,34,33,36,31,38,29,40,27,42,25,44,23,46,21,48,19,50,17,52,15,54,13,56,11,58,9,60,7,62,5,64,3,66,1]t
71	[36,33,38,31,40,29,42,27,44,25,46,23,48,21,50,19,52,17,54,15,56,13,58,11,60,9,62,7,64,5,66,3,68,1,35,34,37,32,39,30,41,28,43,26,45,24,47,22,49,20,51,18,53,16,55,14,57,12,59,10,61,8,63,6,65,4,67,2,69]t
73	[37,34,39,32,41,30,43,28,45,26,47,24,49,22,51,20,53,18,55,16,57,14,59,12,61,10,63,8,65,6,67,4,69,2,71,36,35,38,33,40,31,42,29,44,27,46,25,48,23,50,21,52,19,54,17,56,15,58,13,60,11,62,9,64,7,66,5,68,3,70,1]t
75	[38,35,40,33,42,31,44,29,46,27,48,25,50,23,52,21,54,19,56,17,58,15,60,13,62,11,64,9,66,7,68,5,70,3,72,1,37,36,39,34,41,32,43,30,45,28,47,26,49,24,51,22,53,20,55,18,57,16,59,14,61,12,63,10,65,8,67,6,69,4,71,2,73]t
77	[39,36,41,34,43,32,45,30,47,28,49,26,51,24,53,22,55,20,57,18,59,16,61,14,63,12,65,10,67,8,69,6,71,4,73,2,75,38,37,40,35,42,33,44,31,46,29,48,27,50,25,52,23,54,21,56,19,58,17,60,15,62,13,64,11,66,9,68,7,70,5,72,3,74,1]t
79	[40,37,42,35,44,33,46,31,48,29,50,27,52,25,54,23,56,21,58,19,60,17,62,15,64,13,66,11,68,9,70,7,72,5,74,3,76,1,39,38,41,36,43,34,45,32,47,30,49,28,51,26,53,24,55,22,57,20,59,18,61,16,63,14,65,12,67,10,69,8,71,6,73,4,75,2,77]t
81	[41,38,43,36,45,34,47,32,49,30,51,28,53,26,55,24,57,22,59,20,61,18,63,16,65,14,67,12,69,10,71,8,73,6,75,4,77,2,79,40,39,42,37,44,35,46,33,48,31,50,29,52,27,54,25,56,23,58,21,60,19,62,17,64,15,66,13,68,11,70,9,72,7,74,5,76,3,78,1]t
83	[42,39,44,37,46,35,48,33,50,31,52,29,54,27,56,25,58,23,60,21,62,19,64,17,66,15,68,13,70,11,72,9,74,7,76,5,78,3,80,1,41,40,43,38,45,36,47,34,49,32,51,30,53,28,55,26,57,24,59,22,61,20,63,18,65,16,67,14,69,12,71,10,73,8,75,6,77,4,79,2,81]t
85	[43,40,45,38,47,36,49,34,51,32,53,30,55,28,57,26,59,24,61,22,63,20,65,18,67,16,69,14,71,12,73,10,75,8,77,6,79,4,81,2,83,42,41,44,39,46,37,48,35,50,33,52,31,54,29,56,27,58,25,60,23,62,21,64,19,66,17,68,15,70,13,72,11,74,9,76,7,78,5,80,3,82,1]t
87	[44,41,46,39,48,37,50,35,52,33,54,31,56,29,58,27,60,25,62,23,64,21,66,19,68,17,70,15,72,13,74,11,76,9,78,7,80,5,82,3,84,1,43,42,45,40,47,38,49,36,51,34,53,32,55,30,57,28,59,26,61,24,63,22,65,20,67,18,69,16,71,14,73,12,75,10,77,8,79,6,81,4,83,2,85]t
89	[45,42,47,40,49,38,51,36,53,34,55,32,57,30,59,28,61,26,63,24,65,22,67,20,69,18,71,16,73,14,75,12,77,10,79,8,81,6,83,4,85,2,87,44,43,46,41,48,39,50,37,52,35,54,33,56,31,58,29,60,27,62,25,64,23,66,21,68,19,70,17,72,15,74,13,76,11,78,9,80,7,82,5,84,3,86,1]t
91	[46,43,48,41,50,39,52,37,54,35,56,33,58,31,60,29,62,27,64,25,66,23,68,21,70,19,72,17,74,15,76,13,78,11,80,9,82,7,84,5,86,3,88,1,45,44,47,42,49,40,51,38,53,36,55,34,57,32,59,30,61,28,63,26,65,24,67,22,69,20,71,18,73,16,75,14,77,12,79,10,81,8,83,6,85,4,87,2,89]t
93	[47,44,49,42,51,40,53,38,55,36,57,34,59,32,61,30,63,28,65,26,67,24,69,22,71,20,73,18,75,16,77,14,79,12,81,10,83,8,85,6,87,4,89,2,91,46,45,48,43,50,41,52,39,54,37,56,35,58,33,60,31,62,29,64,27,66,25,68,23,70,21,72,19,74,17,76,15,78,13,80,11,82,9,84,7,86,5,88,3,90,1]t
95	[48,45,50,43,52,41,54,39,56,37,58,35,60,33,62,31,64,29,66,27,68,25,70,23,72,21,74,19,76,17,78,15,80,13,82,11,84,9,86,7,88,5,90,3,92,1,47,46,49,44,51,42,53,40,55,38,57,36,59,34,61,32,63,30,65,28,67,26,69,24,71,22,73,20,75,18,77,16,79,14,81,12,83,10,85,8,87,6,89,4,91,2,93]t
97	[49,46,51,44,53,42,55,40,57,38,59,36,61,34,63,32,65,30,67,28,69,26,71,24,73,22,75,20,77,18,79,16,81,14,83,12,85,10,87,8,89,6,91,4,93,2,95,48,47,50,45,52,43,54,41,56,39,58,37,60,35,62,33,64,31,66,29,68,27,70,25,72,23,74,21,76,19,78,17,80,15,82,13,84,11,86,9,88,7,90,5,92,3,94,1]t
99	[50,47,52,45,54,43,56,41,58,39,60,37,62,35,64,33,66,31,68,29,70,27,72,25,74,23,76,21,78,19,80,17,82,15,84,13,86,11,88,9,90,7,92,5,94,3,96,1,49,48,51,46,53,44,55,42,57,40,59,38,61,36,63,34,65,32,67,30,69,28,71,26,73,24,75,22,77,20,79,18,81,16,83,14,85,12,87,10,89,8,91,6,93,4,95,2,97]t