Enumeration of small nonisomorphic 1-rotational twofold triple systems
Chee, Yeow Meng
Royle, Gordon F.
Date of Issue1992
School of Physical and Mathematical Sciences
In this paper, twofold triple systems of order v are enumerated for all v ≤ 19. The existence of TS(v , 2)'s (all terms are defined in §2) is completely settled; the condition v -0 or 1 (mod 3) is known to be both necessary and sufficient . On the other hand, enumeration efforts have not enjoyed such success. In fact, the exact number of painvise nonisomorphic TS(v, 2)'s, denoted N(v) , has been determined only for v 5 10. In particular, we have N(3) = N(4) = 1 (trivial), N(6) = 1 , N(7) = 4 , N(9) = 36 [12, 81, and N(10) = 960 [l, 31. One reason for the unavailability of such enumeration results for higher values of v is the inherent computational complexity of the problem that leads to a combinatorial explosion effect. To curb this combinatorial explosion, extra conditions are often imposed to enumerate interesting classes of designs. One such condition involves specifying automorphisms that the desired designs must possess.
Mathematics of computation
© 1992 American Mathematical Society. This paper was published in Mathematics of Computation and is made available as an electronic reprint (preprint) with permission of American Mathematical Society. The paper can be found at the following official URL: http://www.jstor.org/stable/2153077. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.