3 research outputs found
Semi-cyclic holey group divisible designs with block size three and applications to sampling designs and optical orthogonal codes
We consider the existence problem for a semi-cyclic holey group divisible
design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of
type (n,m^t). When t is odd and n\neq 8 or t is doubly even and t\neq 8, the
existence problem is completely solved; when t is singly even, many infinite
families are obtained. Applications of our results to two-dimensional balanced
sampling plans and optimal two-dimensional optical orthogonal codes are also
discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1304.328
Leaves for packings with block size four
We consider maximum packings of edge-disjoint -cliques in the complete
graph . When or , these are simply block
designs. In other congruence classes, there are necessarily uncovered edges; we
examine the possible `leave' graphs induced by those edges. We give particular
emphasis to the case or , when the leave is
-regular. Colbourn and Ling settled the case of Hamiltonian leaves in this
case. We extend their construction and use several additional direct and
recursive constructions to realize a variety of -regular leaves. For various
subsets , we establish explicit lower bounds on
to guarantee the existence of maximum packings with any possible leave
whose cycle lengths belong to .Comment: 19 pages plus supplementary fil
Group divisible designs with block size 4 and type g^u m^1 - II
We show that the necessary conditions for the existence of 4-GDDs of type g^u
m^1 are sufficient for g congruent to 0 (mod h), h = 39, 51, 57, 69, 87, 93,
and for g = 13, 17, 19, 23, 25, 29, 31 and 35. More generally, we show that for
all g congruent to 3 (mod 6), the possible exceptions occur only when u = 8 and
g is not divisible by any of 9, 15, 21, 33, 39, 51, 57, 69, 87 or 93.
Consequently we are able to extend the known spectrum for g congruent to 1 and
g congruent to 5 (mod 6). Also we complete the spectrum for 4-GDDs of type
(3a)^4 (6a)^1 (3b)^1.Comment: 106 pages, including 91-page Appendix. Abridged submitted for
publicatio