In this article, we establish the existence of an LHMTS(mv) for v ≡ 2 (mod 6) and m ≡ 3 (mod 6). Thus there exists an LHMTS(mv) if and only if v(v − 1)m2 ≡ 0 (mod 3) except possibly for v = 6, m ≡ 1,5 (mod 6) and m ≠ 1. In the similar way, the existence of LHDTS(mv) is completely determined, i.e., there exists an LHDTS(mv) if and only if v(v − 1)m2 ≡ 0 (mod 3).
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.