Direct constructions for certain types of HMOLS
The authors give direct constructions for 16 new orders of 3-HMOLS, 7 orders of 4-HMOLS, 2 orders of 6-HMOLS, 34 orders of 7-HMOLS all with equal sized holes. In addition, they give constructions for 4 new orders of 3-HMOLS of type \((2^n3^1)\) and 7 new orders of 4-HMOLS of type \((2^n3^1)\). Prior results plus some of the results of this paper can be summarized as follows: (1) if \(n\geq 5\), then there exist 3-HMOLS of type \(h^n\), except for \((h,n)=(1,6)\) and possibly for \((h,n)\in \{(1,10), (3,6), (3, 18), (3,28),(3,34),(6,18),(6,19),(6,23)\}\), (2) there exist 7-HMOLS of type \(3^p\) for all primes \(p\equiv 1\) \(\pmod 6\), with \(30< p<400\), and (3) there exist 3-HMOLS of type \((2^n3^1)\) for all \(n \geq 6\) except possibly for \(n\in\{6,9,10, 12,14,15,17, 21,24,26, 27\}\).
scientific article; zbMATH DE number 1135953