Mathematical Problems in Engineering

Research Article

Some New Dimensions to Construct Economical Circular Weakly Balanced Neighbor Robust Designs

Table 5

MCWBNDs-II for ≤100, 4>k1 ≤ 10, and 3≤k2 ≤ 9.


	k1	k2	Sets of shifts	En

16	4	3	[3,4,7]+[1,5]	0.75
24	4	3	[2,10,11]+[5,7,8]+[6,15]	0.75
32	4	3	[2,9,20]+[6,7,15]+[8,10,11]+[13,14]	0.71
40	4	3	[3,17,18]+[6,8,25]+[9,13,14]+[10,11,12]+[5,16]	0.75
48	4	3	[6,20,21]+[7,9,30]+[10,11,19]+[12,14,17]+[13,15,16]+[22,23]	0.75
56	4	3	[3,16,35]+[7,19,24]+[10,11,27]+[12,14,25]+[15,18,22]+[9,17,26]+[13,20]	0.75
64	4	3	[3,19,40]+[9,22,25]+[11,15,28]+[13,14,30]+[16,18,29]+[12,17,31]+[6,26,27]+[20,21]	0.75
72	4	3	[3,22,45]+[7,25,34]+[9,20,35]+[14,15,30]+[17,18,21]+[19,23,29]+[10,24,33]+[11,26,31]+[12,28]	0.75
80	4	3	[3,25,50]+[7,29,38]+[11,28,32]+[14,15,39]+[13,26,37]+[20,21,23]+[22,24,33]+[8,31,36]+[17,18,35]+[19,27]	0.75
88	4	3	[3,28,55]+[12,34,35]+[14,22,39]+[15,24,43]+[16,26,38]+[21,23,25]+[9,36,42]+[18,29,30]+[10,32,41]+[20,27,37]+[17,31]	0.75
96	4	3	[3,31,60]+[7,40,44]+[19,28,39]+[14,27,42]+[17,26,45]+[22,23,30]+[24,25,32]+[20,29,46]+[11,34,47]+[16,33,38]+[12,37,41]+[18,35]	0.75
18	5	3	[2,6,4,5]+[7,8]	0.78
48	5	3	[4,5,17,21]+[8,9,10,14]+[6,11,13,16]+[15,19,20,30]+[22,23]	0.80
58	5	3	[20,25,26,28]+[8,10,13,23]+[11,12,14,15]+[3,16,18,19]+[5,7,21,24]+[22,27]	0.80
88	5	3	[11,21,23,30]+[12,14,26,27]+[10,13,28,31]+[5,18,25,39]+[15,16,19,36]+[8,20,24,29]+[32,34,38,55]+[35,37,40,42]+[41,43]	0.79
98	5	3	[5,6,41,42]+[9,11,37,38]+[17,19,22,24]+[10,26,27,28]+[14,20,21,31]+[13,18,29,30]+[34,35,46,48]+[39,40,45,47]+[2,15,36,44]+[32,43]	0.79
32	6	3	[2,4,5,7,13]+[8,9,10,11,20]+[14,15]	0.82
56	6	3	[3,4,6,7,35]+[11,20,22,23,26]+[5,8,9,15,17]+[14,18,19,24,25]+[16,27]	0.76
80	6	3	[4,6,14,22,32]+[11,12,38,39,50]+[13,15,16,17,18]+[21,23,26,33,37]+[24,28,31,34,35]+[5,7,9,27,29]+[25,36]	0.82
50	7	3	[2,3,5,7,9,23]+[11,13,14,15,20,21]+[10,12,16,17,18,19]+[22,24]	0.85
64	7	3	[3,4,6,7,11,31]+[10,12,13,16,28,40]+[15,17,19,20,21,22]+[8,18,23,25,26,27]+[29,30]	0.76
24	8	3	[2,4,5,6,8,7,15]+[10,11]	0.84
40	8	3	[2,3,4,5,6,7,12]+[10,11,14,16,17,19,25]+[13,18]	0.86
56	8	3	[3,4,6,7,8,12,15]+[13,16,20,22,24,27,35]+[9,10,14,17,18,19,23]+[25,26]	0.86
72	8	3	[2,5,6,7,8,10,33]+[11,12,13,16,18,20,45]+[14,17,19,21,22,23,24]+ [25,26,28,29,30,32,31]+[34,35]	0.87
88	8	3	[4,5,6,7,8,15,41]+[9,10,11,12,13,14,18]+[19,20,21,22,23,26,29]+[27,28,30,31,34,35,55]+[25,32,36,37,38,39,40]+[42,43]	0.87
26	9	3	[2,3,4,6,7,8,9,12]+[10,11]	0.86
80	9	3	[6,7,8,9,9,24,31,34,36]+[11,12,13,14,15,17,18,50]+ [3,19,20,21,22,23,25,26]+[16,27,28,29,32,33,35,38]+[37,39]	0.88
98	9	3	[4,5,6,7,9,10,26,29]+[15,16,17,18,20,23,31,42]+[11,12,13,24,25,34,37,39]+[28,30,32,33,35,36,40,41]+[21,22,27,38,44,45,46,48]+[43,47]	0.88
48	10	3	[4,5,6,7,8,9,11,21,22]+[2,12,13,14,16,17,19,20,30]+[15,23]	0.88
88	10	3	[3,5,6,7,8,9,10,12,26]+[14,15,16,17,18,19,20,21,32]+ [22,24,25,27,28,29,30,31,35]+[23,36,37,38,39,40,41,42,55]+ [34,43]	0.89
40	5	4	[1,17,18,4]+[6,7,8,9]+[16,12,13,14]+[2,3,19]	0.71
50	5	4	[6,2,17,1]+[7,3,18,4]+[8,14,20,22]+[10,15,21,23]+[19,16,24]	0.79
80	5	4	[36,2,3,4]+[32,6,8,9]+[21,12,13,14]+[16,17,18,19]+[11,22,23,24]+[26,27,28,29]+[7,1,33,34]+[37,38,39]	0.75
90	5	4	[5,10,31,41]+[4,27,28,29]+[14,15,20,30]+[16,17,18,38]+[13,21,24,25]+[9,12,26,35]+[33,34,37,44]+[36,39,40,42]+[19,22,43]	0.80
34	6	4	[3,4,5,6,14]+[9,10,12,13,16]+[7,11,15]	0.83
58	6	4	[4,5,6,20,21]+[8,9,10,11,13]+[16,17,18,22,28]+[14,23,24,25,27]+[12,19,26]	0.83
82	6	4	[4,5,6,31,33]+[9,10,11,12,32]+[14,15,16,17,18]+[21,22,23,39,40]+[26,27,28,29,30]+[13,34,35,37,38]+[20,25,36]	0.79
24	7	4	[3,4,6,7,15,11]+[5,8,10]	0.85
66	7	4	[10,16,18,23,27,31]+[5,9,11,12,13,14]+[8,20,21,22,28,32]+[15,17,19,24,25,26]+ [4,29,30]	0.85
80	7	4	[4,5,6,7,25,31]+[9,10,11,13,14,15]+[18,19,20,21,34,36]+[22,23,24,27,28,33]+[29,32,35,38,39,50]+[16,26,37]	0.85
26	8	4	[3,5,6,7,10,8,11]+[4,9,12]	0.86
42	8	4	[2,3,5,6,7,8,10]+[13,14,16,15,17,19,20]+[9,11,18]	0.87
58	8	4	[4,5,6,7,8,12,13]+[10,11,14,15,16,20,28]+[18,19,23,21,24,25,27]+[9,22,26]	0.87
74	8	4	[4,5,6,7,8,10,33]+[11,12,14,15,17,34,36]+[27,18,19,22,23,24,13]+ [25,26,28,29,30,31,32]+[16,20,35]	0.87
90	8	4	[7,8,17,24,36,41,42]+[9,10,11,12,13,15,16]+[19,20,21,22,23,25,32]+[31,26,27,28,29,30,6]+[33,34,35,37,38,39,40]+[2,43,44]	0.87
64	9	4	[4,5,7,9,17,20,23,40]+[11,12,13,14,15,16,18,19]+[8,21,22,25,26,27,30,31]+[6,28,29]	0.88
82	9	4	[3,4,5,6,6,7,8,9,38]+[13,14,15,16,17,18,19,40]+[24,25,26,27,28,35,34,36]+[21,22,23,29,31,30,33,37]+[10,3239]	0.88
50	10	4	[6,7,8,9,11,12,13,15,14]+[22,10,16,17,18,19,21,20,4]+[2,23,24]	0.89
90	10	4	[5,6,7,8,9,11,12,13,15]+[14,16,17,18,19,21,20,22,23]+[24,26,27,28,29,30,32,31,40]+[33,34,35,36,37,39,38,41,42]+ [2,43,44]	0.89
24	6	5	[6,7,8,10,15]+[3,4,5,11]	0.84
48	6	5	[6,16,19,23,30]+[7,8,9,11,12]+[13,15,17,20,21]+[3,4,5,14]	0.70
72	6	5	[2,3,5,30,31]+[8,9,10,11,28]+[16,17,32,33,34]+[20,22,23,25,35]+[13,24,26,29,45]+[14,15,18,21]	0.84
96	6	5	[3,4,5,22,60]+[9,10,11,12,46]+[14,15,16,17,21]+[7,19,20,23,26]+[28,29,30,42,45]+[31,32,35,33,37]+[25,27,43,44,47]+[38,39,40,41]	0.84
26	7	5	[5,6,7,11,12,8]+[2,4,9,10]	0.86
40	7	5	[3,4,5,6,7,13]+[9,10,12,14,16,18]+[11,17,19,25]	0.86
82	7	5	[3,4,5,7,30,31]+[9,10,11,12,15,24]+[16,20,21,22,32,40]+[18,23,25,26,27,28]+[8,19,29,33,34,35]+[36,37,38,39]	0.86
96	7	5	[3,4,5,7,30,46]+[9,10,11,13,14,31]+[19,20,21,24,45,47]+[23,26,27,28,32,38]+[22,29,33,35,34,37]+[15,17,25,40,41,42]+[39,43,44,60]	0.86
48	9	5	[2,3,4,5,6,8,9,10]+[12,13,14,15,16,20,17,30]+[11,19,21,22]	0.89
66	9	5	[3,4,5,6,7,8,9,22]+[11,12,14,15,16,17,19,18]+[20,21,23,24,25,26,27,31]+[28,29,30,32]	0.89
32	10	5	[3,4,5,6,7,8,9,10,11]+[13,14,15,20]	0.89
72	10	5	[3,4,5,6,7,8,9,10,18]+[11,12,13,14,17,19,16,21,20]+[23,24,26,25,28,29,31,35,45]+[30,32,33,34]	0.89
42	7	6	[3,4,5,6,7,15]+[10,11,12,13,14,16]+[9,17,18,19,20]	0.87
56	7	6	[2,3,4,5,6,35]+[9,10,15,17,26,27]+[13,14,16,18,19,20]+[11,22,23,24,25]	0.79
98	7	6	[3,4,5,6,7,15]+[10,11,12,13,14,16]+[38,18,19,20,21,9]+[22,23,25,26,27,28]+[32,33,34,35,40,48]+[31,36,37,39,42,43]+[41,44,45,46,47]	0.86
32	8	7	[9,10,11,13,14,15,20]+[2,3,5,6,7,8]	0.89
48	8	7	[30,16,20,21,22,23,9]+[10,11,12,13,14,15,17]+[2,5,6,7,8,19]	0.89
64	8	7	[2,3,5,6,7,9,31]+[10,11,12,14,15,18,40]+[17,20,25,27,28,29,30]+[13,19,21,22,23,26]	0.87
80	8	7	[2,3,4,5,7,8,50]+[12,13,14,15,20,36,39]+[16,19,21,23,24,25,26]+[22,32,33,34,35,37,38]+[17,18,27,28,29,31]	0.88
96	8	7	[5,6,7,32,38,41,60]+[10,11,12,13,14,15,20]+[18,19,21,22,23,25,47]+[28,29,31,40,42,45,46]+[4,8,33,34,35,37,39]+[16,24,26,30,43,44]	0.83
34	9	7	[4,5,6,8,9,10,11,12]+[2,7,13,15,14,16]	0.89
88	9	7	[2,4,5,6,8,9,12,41]+[13,14,15,17,18,25,43,28]+[23,26,27,30,32,34,37,39]+[21,22,24,29,31,35,36,55]+[10,19,20,38,40,42]	0.89
72	9	8	[3,4,5,6,7,9]+[11,12,13,14,15,16]+[20,23,24,26,25,31]+[21,22,28,29,30]	0.89
90	9	8	[3,4,6,7,8,9,10,41]+[13,14,15,16,17,18,31,44]+[23,24,25,26,30,39,40,42]+[27,28,29,34,33,35,36,37]+[5,19,20,22,32,38,43]	0.89
58	10	8	[2,3,4,5,6,7,8,9,13]+[14,15,16,17,18,19,20,22,23]+[12,21,24,25,26,27,28]	0.91
98	10	8	[3,4,5,6,7,8,9,10,44]+[13,14,15,16,17,18,19,31,41]+[24,25,26,27,28,29,30,40,42]+[20,21,32,33,34,35,37,38,43]+[22,36,39,45,46,47,48]	0.86
40	10	9	[3,4,5,6,7,8,9,17,19]+[10,11,12,13,14,16,18,25]	0.91
80	10	9	[2,3,4,5,6,7,8,9,35]+[12,13,14,15,16,17,19,18,25]+[20,22,23,24,26,27,28,29,31]+[21,32,33,34,36,37,38,39]	0.91