Mathematical Problems in Engineering

Research Article

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

Table 6

MCWBNDs-II for ≤ 100, 5≤k1 ≤ 10, 4<k2 ≤ 9, and 3≤k3 ≤ 7.


	k1	k2	k3	Sets of shifts	En

26	5	4	3	[3,5,7,9]+[4,10,11]+[8,12]	0.76
56	5	4	3	[2,4,14,35]+[9,10,11,19]+[8,12,15,16]+[22,23,24,25]+[13,17,20]+[26,27]	0.79
58	5	4	3	[4,5,19,27]+[7,9,12,24]+[10,13,16,18]+[17,20,22,43]+[8,23,25]+[21,26]	0.79
96	5	4	3	[4,5,40,45]+[10,16,27,35]+[15,19,25,28]+[18,22,26,29]+[34,38,43,44]+[17,21,23,24]+[7,20,31,32]+[37,39,42,60]+[13,30,41]+[46,47]	0.79
98	5	4	3	[4,12,32,47]+[10,16,17,46]+[13,15,21,44]+[18,19,20,33]+[24,34,43,73]+[7,26,29,30]+[11,23,27,35]+[37,38,40,45]+[14,41,42]+ [31,39]	0.80
40	6	4	3	[2,3,7,8,19]+[10,11,12,13,25]+[6,14,16]+[17,18]	0.81
64	6	4	3	[3,6,8,15,31]+[10,11,12,13,14]+[16,17,20,28,40]+[19,21,22,23,25]+ [9,26,27]+[29,30]	0.82
88	6	4	3	[2,4,6,20,55]+[9,10,11,12,38]+[17,18,41,42,43]+[23,24,31,36,40]+[27,28,29,30,37]+ [5,13,14,21,32]+ [16,26,39]+[34,35]	0.82
58	7	4	3	[4,5,6,7,15,18]+[12,14,16,17,21,28]+[9,10,20,23,25,27]+[11,22,24]+[19,26]	0.82
72	7	4	3	[4,5,6,9,22,24]+[8,12,15,26,45,31]+[17,18,19,20,21,33]+[11,13,23,30,25,32]+[14,28,29]+[34,35]	0.84
42	6	5	3	[3,4,6,7,20]+[12,13,15,16,17]+[8,9,10,14]+[18,19]	0.81
66	6	5	3	[3,4,6,20,31]+[9,10,11,12,16]+[18,25,26,30,32]+[19,22,23,24,29]+[7,13,14,27]+[21,28]	0.82
90	6	5	3	[3,4,6,31,44]+[9,10,12,17,34]+[24,27,35,36,40]+[7,19,20,21,22]+[25,26,32,33,41]+[28,29,30,38,39]+[13,14,15,37]+[42,43]	0.82
32	7	5	3	[2,3,5,6,7,8]+[10,11,14,20]+[13,15]	0.82
34	8	5	3	[3,4,8,9,11,15,16]+[5,6,10,12]+[13,14]	0.83
50	8	5	3	[7,8,10,11,15,19,24]+[3,9,12,16,17,20,21]+[4,13,14,18]+[22,23]	0.85
66	8	5	3	[5,6,7,8,10,12,17]+[11,14,15,16,25,21,26]+[9,13,19,20,22,23,24]+[27,28,29,30]+[31,32]	0.86
82	8	5	3	[4,5,6,7,8,25,26]+[10,15,16,27,28,29,30]+[18,19,20,21,22,23,24]+[3,13,14,31,32,34,35]+ [36,38,39,40]+[33,37]	0.81
34	7	6	3	[7,8,9,11,13,14]+[2,4,5,10]+[15,16]	0.83
48	7	6	3	[3,5,6,7,11,15]+[8,10,14,19,21,22]+[9,16,17,20,30]+[13,23]	0.84
74	7	6	3	[3,5,6,7,20,31]+[12,13,14,27,35,36]+[16,17,18,19,29,34]+[10,23,24,25,28,30]+[4,21,22,26]+[32,33]	0.85
90	7	6	3	[3,4,7,10,32,33]+[9,11,13,14,16,21]+[19,20,25,35,36,37]+[23,24,26,27,28,30]+[15,18,29,34,38,44]+[17,31,39,40]+[42,43]	0.86
56	9	6	3	[6,7,8,9,10,11,22,35]+[15,16,17,18,19,20,24,25]+[2,5,12,13,23]+[26,27]	0.86
74	9	6	3	[6,7,8,13,19,29,30,31]+[11,12,14,15,17,18,20,32]+[21,22,23,25,27,26,28,34]+[2,4,10,24,33]+[35,36]	0.90
40	9	7	3	[4,5,6,7,8,9,13,25]+[2,11,14,16,17,19]+[18,10]	0.86
58	9	7	3	[3,4,5,6,7,8,9,14]+[10,11,12,13,15,17,18,19]+[23,24,25,26,27,28]+[20,22]	0.87
42	10	7	3	[3,4,6,8,9,10,11,20,12]+[7,13,14,16,15,17]+[18,19]	0.87
82	10	7	3	[3,4,5,6,7,8,9,10,28]+[13,14,15,16,17,18,19,20,21]+[22,23,24,25,26,27,30,29,39]+[33,34,35,36,37,40]+[32,38]	0.89
42	9	8	3	[6,7,8,9,11,12,13,14]+[2,3,10,15,16,17,20]+[18,19]	0.87
96	9	8	3	[4,5,6,7,8,9,10,45]+[14,15,16,17,18,27,35,37]+[19,20,21,22,23,24,25,26]+[28,29,30,31,32,34,33,60]+[38,39,41,40,42,43,44]+[46,47]	0.88
64	10	8	3	[2,4,5,6,7,8,9,10,12]+[14,15,16,17,18,19,20,22,40]+[21,23,25,26,27,28,29]+[30,31]	0.88
66	10	9	3	[3,4,5,6,7,8,9,10,12]+[14,15,16,17,19,20,21,31,32]+[18,22,23,24,26,27,28,29]+[25,30]	0.89
48	7	5	4	[4,5,6,7,11,12]+[8,9,13,14,20,30]+[17,19,21,23]+[10,15,22]	0.84
34	7	5	4	[7,8,9,12,10,16]+[3,4,11,15]+[5,13,14]	0.83
50	7	6	4	[3,4,5,6,7,23]+[11,12,13,16,14,24]+[15,17,18,20,21]+[8,19,22]	0.76
90	7	5	4	[4,5,6,7,21,44]+[8,11,12,13,14,31]+[18,19,20,22,41,43]+[25,26,27,28,32,33]+[16,24,29,34,35,40]+[36,37,38,39]+[15,23,42]	0.85
50	7	6	4	[3,4,5,6,7,24]+[11,12,13,17,14,23]+[15,16,20,19,21]+[8,18,22]	0.84
64	7	6	4	[4,5,6,7,8,31]+[11,12,13,14,28,40]+[16,17,18,19,21,22]+[20,23,26,27,30]+[9,25,29]	0.90
40	9	6	4	[4,5,6,7,8,9,13,25]+[12,14,16,17,19]+[10,11,18]	0.86
58	9	6	4	[5,7,8,9,14,16,26,27]+[10,11,12,13,15,17,18,19]+[20,21,22,23,24]+[3,25,28]	0.87
42	9	7	4	[5,6,7,8,9,10,17,18]+[11,12,13,14,16,15]+[2,19,20]	0.87
64	10	7	4	[3,4,5,6,7,8,9,10,11]+[15,16,17,18,19,20,21,22,30]+[12,13,23,25,26,27]+[29,31,40]	0.88
80	9	8	4	[3,4,5,6,7,8,9,36]+[13,14,15,16,17,28,18,29]+[20,24,25,26,27,32,33,34]+[21,22,23,35,38,39,50]+[11,31,37]	0.90
96	9	8	4	[4,5,6,7,8,10,26,27]+[13,14,15,16,17,20,42,43]+[2,18,22,23,24,25,38,39]+[60,29,30,31,32,34,35,28]+[37,40,44,41,46,47]+[19,21]	0.85
98	9	8	4	[4,5,6,7,8,9,27,29]+[13,14,15,16,17,18,45,46]+[19,21,22,23,24,25,35,26]+[28,30,31,32,33,34,38,48]+[36,37,40,41,43,42,44]+[10,39,47]	0.88
66	10	8	4	[3,4,5,6,7,8,9,10,12]+[14,15,16,17,19,18,26,29,31]+[21,23,24,25,27,28,30]+[11,22,32]	0.88
48	10	9	4	[3,5,6,7,9,10,21,11,22]+[12,13,14,15,16,19,17,30]+[4,20,23]	0.89
88	10	9	4	[3,4,5,6,7,8,9,10,34]+[13,14,15,16,17,18,19,20,32]+[23,24,25,26,27,28,29,30,31]+[36,37,38,39,40,42,43,55]+[11,35,41]	0.90
66	7	6	5	[5,6,7,8,9,28]+[2,4,12,13,15,19]+[23,18,20,21,22,17]+[16,24,25,26,27]+[29,30,31,32]	0.85
80	7	6	5	[3,4,5,6,11,50]+[13,14,19,33,35,39]+[17,18,20,21,32,37]+[22,23,25,26,27,28]+[16,29,31,34,38]+[8,10,24,36]	0.86
82	7	6	5	[4,6,7,8,18,36]+[5,9,13,14,15,25]+[10,16,17,20,38,61]+[22,23,24,27,28,29]+[26,30,31,32,33]+[34,35,37,39]	0.86
40	8	6	5	[6,7,8,9,12,14,19]+[2,3,10,11,13]+[16,17,18,25]	0.86
56	8	6	5	[3,4,5,10,26,27,35]+[9,11,13,14,16,17,24]+[15,18,20,22,25]+[6,7,19,23]	0.86
72	8	6	5	[4,5,6,7,8,9,31]+[12,13,15,16,21,28,29]+[19,22,23,24,32,33,45]+[17,25,26,30,35]+[3,14,20,34]	0.87
88	8	6	5	[2,4,5,6,7,8,55]+[13,14,15,16,21,42,43]+[18,19,20,22,23,24,40]+[29,30,31,32,34,39,41]+[27,35,36,37,38]+[11,17,25,26]	0.87
42	9	6	5	[5,6,7,8,9,20,12,13]+[14,15,16,17]+[2,10,11,18]	0.79
90	9	6	5	[4,5,6,7,8,9,10,44]+[13,14,16,17,18,20,42,41]+[24,25,26,28,38,39,40,45]+[27,29,30,31,32,34,33,60]+[2,15,22,19,37]+[35,43,46,47]	0.80
42	8	7	5	[2,4,5,6,7,8,9]+[15,11,12,13,14,16]+[17,18,19,20]	0.87
58	8	7	5	[3,4,5,6,7,8,23]+[10,12,13,14,16,17,25]+[15,18,19,20,21,22]+[24,26,27,28]	0.80
74	8	7	5	[3,4,6,7,8,9,35]+[12,13,14,15,16,31,36]+[24,26,27,28,29,32,34]+[18,19,20,21,23,30]+[5,10,25,33]	0.85
90	8	7	5	[4,5,6,7,8,16,41]+[9,10,11,12,14,15,17]+[19,21,22,23,25,24,28]+[29,30,32,31,34,43,44]+[13,20,35,36,37,38]+[33,39,40,42]	0.87
82	9	7	5	[3,4,5,6,7,9,18,28]+[11,12,13,15,17,19,32,35]+[22,23,24,25,26,27,30,61]+ [16,20,29,31,33,34]+ [36,37,38,39]	0.87
98	9	7	5	[3,4,5,6,7,9,14,48]+[12,13,15,16,17,22,44,47]+[25,26,27,30,39,40,41,42]+[28,29,31,33,35,34,36,45]+[19,20,21,37,38,43]+[8,11,32,46]	0.88
66	10	7	5	[3,4,5,6,7,8,9,10,12]+[11,19,20,22,23,24,25,26,27]+[15,16,17,18,21,32]+[28,29,30,31]	0.82
82	9	8	5	[3,4,5,6,7,8,9,38]+[13,14,15,16,18,26,19,33]+[11,17,20,21,22,23,24,25]+[28,29,30,31,32,34,35]+[36,37,39,40]	0.90
48	10	8	5	[4,5,6,7,8,9,11,21,22]+[13,14,16,17,19,23,30]+[2,10,15,20]	0.88
88	10	8	5	[3,4,5,6,7,8,9,10,34]+[13,14,15,16,17,18,19,20,32]+[22,23,24,25,27,28,29,30,35]+[26,31,36,37,38,40,55]+[39,41,42,43]	0.90
50	10	9	5	[6,7,8,9,11,12,13,15,14]+[2,3,4,16,17,18,19,20]+[21,22,23,24]	0.89
90	10	9	5	[3,4,5,6,7,8,9,10,36]+[13,14,15,16,17,18,19,37,20]+[22,24,25,26,27,28,29,30,38]+[23,31,32,33,34,35,39,42]+[40,41,43,44]	0.90
64	9	7	6	[3,4,5,6,7,8,9,20]+[11,12,13,14,15,16,18,19]+[22,23,25,30,31,40]+[17,26,27,28,29]	0.88
82	9	7	6	[3,4,5,6,7,8,9,38]+[12,14,15,16,17,18,30,31]+[22,24,25,26,27,28,39,34]+ [13,19,23,29,33,37]+[20,32,35,36,40]	0.89
48	9	8	6	[4,5,6,8,11,17,22,20]+[9,10,12,13,14,15,16]+[2,19,21,23,30]	0.89
66	9	8	6	[3,4,5,6,7,8,9,22]+[11,12,14,15,16,17,19,18]+[21,23,24,25,26,28,31]+[13,27,29,30,32]	0.88
50	9	8	7	[5,6,7,8,9,17,21,23]+[10,12,13,14,15,16,18]+[3,11,19,22,20,24]	0.89
74	10	9	7	[3,4,5,6,7,8,9,10,20]+[23,13,14,15,16,17,18,19,12]+[22,24,25,26,27,28,29,30]+[31,32,33,34,35,36]	0.89