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