Holey Perfect Mendelsohn Designs of Type 2^𝑛𝑢¹ with Block Size Four

Table 1

Existence proof of HPMD (2^𝑛𝑢¹) for Lemma 43.

𝑛	𝑢	Justification
26	17-18	Lemma 27
27	17–26	Lemma 28
28, 29	17–21	Lemma 14(b) with 𝑚=7 and 𝑘=0,1
30	17–21	Lemma 12 with 𝑚=6, 𝑠=3,4, and 𝑡=17−21
31	17–21	Lemma 30
32, 33	17–24	Lemma 14(b) with 𝑚=8, 𝑘=0,1
34	17–26	Lemma 15 with 𝑚=7, 𝑘=6, and 1≤𝑡≤5
35, 36	17–28	Lemma 16(b) with 𝑚=7, 𝑘=0,1
37, 38	17–28	Lemma 15 with 𝑚=8, 𝑘=5,6, and 1≤𝑡≤𝑘−1
39–41	17–31	Lemma 17 with 𝑚=7, 𝑘=4,5,6, and 1≤𝑡≤𝑘−1
42, 44	17–32	Lemma 15 with 𝑚=9, 𝑘=6,8, and 1≤𝑡≤𝑘−1
43	17–31	Lemma 15 with 𝑚=9, 𝑘=7, and 1≤𝑡≤𝑘−3