DISCRETA report on

2-(15,3,\lambda) designs

generated from the group TetraTetraedgemidpointsxTetradualxaddcenter

Anton Betten, Evi Haberberger, Reinhard Laue, Alfred Wassermann

Mathematical department, University of Bayreuth

This report is generated from the file KM_TetraTetraedgemidpointsxTetradualxaddcenter_t2_k3.txt . This file is 5767 bytes long.

creation date: Fri Jun 11 14:55:27 MEST 1999

the group TetraTetraedgemidpointsxTetradualxaddcenter of order 12 is generated by the following permutations:

(1 2 3)(5 6 7)(8 9 10)(11 12 13)
(1 2 4)(5 9 8)(6 10 7)(11 12 14)

jump to the Kramer Mesner matrix M 2,3

jump to solution vectors

orbits of TetraTetraedgemidpointsxTetradualxaddcenter on i-sets, i less than or equal to 3
i # of orbits index of first orbit jump
0 1 0 jump to orbits / KM-matrix M0,1
1 4 1 jump to orbits / KM-matrix M1,2
2 13 5 jump to orbits / KM-matrix M2,3
3 46 18 jump to orbits
altogether 64 orbits

orbit representatives of TetraTetraedgemidpointsxTetradualxaddcenter on 0-sets
# representative order of the set-stabilizer
1 (1) {} 12

orbit representatives of TetraTetraedgemidpointsxTetradualxaddcenter on 1-sets
# representative order of the set-stabilizer
1 (2) {15} 12
2 (3) {1} 3
3 (4) {5} 2
4 (5) {11} 3

orbit representatives of TetraTetraedgemidpointsxTetradualxaddcenter on 2-sets
# representative order of the set-stabilizer
1 (6) {11, 15} 3
2 (7) {1, 15} 3
3 (8) {5, 15} 2
4 (9) {1, 2} 2
5 (10) {1, 5} 1
6 (11) {1, 6} 1
7 (12) {1, 11} 3
8 (13) {1, 12} 1
9 (14) {5, 6} 1
10 (15) {5, 10} 4
11 (16) {5, 11} 1
12 (17) {5, 13} 1
13 (18) {11, 12} 2

orbit representatives of TetraTetraedgemidpointsxTetradualxaddcenter on 3-sets
# representative order of the set-stabilizer
1 (19) {11, 12, 15} 2
2 (20) {1, 12, 15} 1
3 (21) {1, 11, 15} 3
4 (22) {5, 13, 15} 1
5 (23) {5, 11, 15} 1
6 (24) {1, 2, 15} 2
7 (25) {1, 5, 15} 1
8 (26) {1, 6, 15} 1
9 (27) {5, 6, 15} 1
10 (28) {5, 10, 15} 4
11 (29) {1, 2, 3} 3
12 (30) {1, 2, 5} 2
13 (31) {1, 2, 6} 1
14 (32) {1, 2, 7} 1
15 (33) {1, 2, 10} 2
16 (34) {1, 2, 11} 1
17 (35) {1, 2, 13} 1
18 (36) {1, 5, 6} 1
19 (37) {1, 5, 7} 1
20 (38) {1, 5, 9} 1
21 (39) {1, 5, 10} 1
22 (40) {1, 5, 11} 1
23 (41) {1, 5, 12} 1
24 (42) {1, 5, 13} 1
25 (43) {1, 5, 14} 1
26 (44) {1, 6, 9} 1
27 (45) {1, 6, 11} 1
28 (46) {1, 6, 12} 1
29 (47) {1, 6, 13} 1
30 (48) {1, 6, 14} 1
31 (49) {1, 11, 12} 1
32 (50) {1, 12, 13} 1
33 (51) {5, 6, 7} 3
34 (52) {5, 6, 8} 2
35 (53) {5, 6, 9} 3
36 (54) {5, 6, 10} 2
37 (55) {5, 6, 11} 1
38 (56) {5, 6, 12} 1
39 (57) {5, 6, 13} 1
40 (58) {5, 6, 14} 1
41 (59) {5, 10, 11} 1
42 (60) {5, 11, 12} 2
43 (61) {5, 11, 13} 1
44 (62) {5, 11, 14} 1
45 (63) {5, 13, 14} 2
46 (64) {11, 12, 13} 3

Kramer Mesner matrix M 0,1 for TetraTetraedgemidpointsxTetradualxaddcenter of size 1 x 4 

((1:4:6:4)
)

Kramer Mesner matrix M 1,2 for TetraTetraedgemidpointsxTetradualxaddcenter of size 4 x 13 

((4:4:6:0:0:0:0:0:0:0:0:0:0)
(0:1:0:3:3:3:1:3:0:0:0:0:0)
(0:0:1:0:2:2:0:0:4:1:2:2:0)
(1:0:0:0:0:0:1:3:0:0:3:3:3)
)

Kramer Mesner matrix M 2,3 for TetraTetraedgemidpointsxTetradualxaddcenter of size 13 x 46 

((3:3:1:3:3:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:3:1:0:0:3:3:3:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:0:0:2:2:0:2:2:4:1:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:0:0:0:0:1:0:0:0:0:2:1:2:2:1:2:2:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:0:0:0:0:0:1:0:0:0:0:1:1:1:0:0:0:1:2:1:1:1:1:1:1:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:0:0:0:0:0:0:1:0:0:0:0:1:1:1:0:0:1:0:1:1:0:0:0:0:2:1:1:1:1:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:0:1:0:0:0:0:0:0:0:0:0:0:0:0:3:0:0:0:0:0:3:0:0:0:0:3:0:0:0:3:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:1:0:0:0:0:0:0:0:0:0:0:0:0:0:1:2:0:0:0:0:0:1:1:1:0:0:1:1:1:1:2:0:0:0:0:0:0:0:0:0:0:0:0:0:0)
(0:0:0:0:0:0:0:0:1:0:0:0:0:0:0:0:0:1:1:1:0:0:0:0:0:1:0:0:0:0:0:0:1:1:1:1:1:1:1:1:0:0:0:0:0:0)
(0:0:0:0:0:0:0:0:0:1:0:0:0:0:0:0:0:0:0:0:4:0:0:0:0:0:0:0:0:0:0:0:0:2:0:2:0:0:0:0:4:0:0:0:0:0)
(0:0:0:0:1:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:1:1:0:0:0:0:1:1:0:0:0:0:0:0:0:1:2:1:0:1:1:1:1:0:0)
(0:0:0:1:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:1:1:0:1:0:0:1:0:0:0:0:0:0:1:0:1:2:1:0:1:1:1:0)
(1:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:0:2:2:0:0:0:0:0:0:0:0:0:1:2:2:1:2)
)

Solutions:

\lambda=1:

0010000001010000000000000000100000100000000010
0010000001010000000000000001000000100000000010
0010000001010000000000000000100010000000000010
0010000001010000000000000001000010000000000010
0010000001000010000000100000000000100000000010
0010000001000010000000100000000010000000000010
0010000001000010000000001000000000100000010000
0010000001000010000000010000000000100000010000
0010000001000010000000001000000010000000010000
0010000001000010000000010000000010000000010000
0010000001010000000000000000010000100000010000
0010000001010000000000000000010010000000010000