An APPTS(29) on the point set {A,B,0,1,2,...,26} with a hole {0,1,2,A,B}, and with the property that the addition of any of the 10 triples from the hole will not generate a Pasch configuration. With the addition of blocks A12 and B02 it becomes a generically labelled APMMPTS(29). The point A is represented as 27 and B as 28. There are no blocks {2,x,x+4} with arithmetic mod 27. 

The {A,B}-cycles are (3,4,7,8,5,6)+6k,  k=0,1,2,3. 

By adding the further triples AB1 and A01 to the APMMPTS(29), the design is converted to an APMMCT(29) with thrice repeated pair A1. 

missing pairs
0 1
0 2
0 27 
0 28
1 2
1 27
1 28
2 27
2 28
27 28

number of missing pairs = 10

list of blocks
0 3 8
0 4 11
0 5 13
0 6 15
0 7 9
0 10 17
0 12 23
0 14 25
0 16 22
0 18 24
0 19 21
0 20 26
1 3 9
1 4 24
1 5 17
1 6 20
1 7 14
1 8 19
1 10 15
1 11 16
1 12 22
1 13 23
1 18 25
1 21 26
2 3 13
2 4 25
2 5 21
2 6 11
2 7 15
2 8 23
2 9 26
2 10 19
2 12 18
2 14 17
2 16 24
2 20 22
3 4 27
3 5 16
3 6 28
3 7 17
3 10 21
3 11 23
3 12 25
3 14 18
3 15 20
3 19 22
3 24 26
4 5 9
4 6 13
4 7 28
4 8 20
4 10 26
4 12 15
4 14 22
4 16 18
4 17 19
4 21 23
5 6 27
5 7 23
5 8 28
5 10 25
5 11 18
5 12 20
5 14 19
5 15 24
5 22 26
6 7 22
6 8 25
6 9 19
6 10 18
6 12 24
6 14 26
6 16 23
6 17 21
7 8 27
7 10 11
7 12 19
7 13 24
7 16 26
7 18 20
7 21 25
8 9 24
8 10 16
8 11 17
8 12 26
8 13 18
8 14 21
8 15 22
9 10 27
9 11 22
9 12 28
9 13 20
9 14 16
9 15 25
9 17 23
9 18 21
10 12 14
10 13 28
10 20 23
10 22 24
11 12 27
11 13 26
11 14 28
11 15 21
11 19 24
11 20 25
12 13 21
12 16 17
13 14 27
13 15 19
13 16 25
13 17 22
14 15 23
14 20 24
15 16 27
15 17 26
15 18 28
16 19 28
16 20 21
17 18 27
17 20 28
17 24 25
18 19 26
18 22 23
19 20 27
19 23 25
21 22 27
21 24 28
22 25 28
23 24 27
23 26 28
25 26 27