منابع مشابه
Some New Symmetric Block Designs EDWARD
In his book [I 1, Marshall Hall gives a table of balanced incomplete block designs with from 3 to 15 replications. It is mentioned there that a solution is unknown as to whether or not there exists a symmetric block design with parameters (v, k, h) = (36, 15, 6) (number 104 in the table). It is the purpose of this paper to show that such a design can in fact be constructed quite simply and to s...
متن کاملAn infinite family of symmetric designs
In this paper, using the construction method of [3], we show that if q>2 is a prime power such that there exists an affine plane of order q -1, then there exists a ~trongly divisible 2 -«q -1)(qh -1), qh-l(q -1), qh-l) design for every h;;. 2. We show that these quasi-residual designs are embeddable, and hence establish the existence of an infinite family of symmetric 2_(qh+l_q + 1, qh, qh-l) d...
متن کاملOn a Characterization of Symmetric Balanced Incomplete Block Designs
All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated...
متن کاملQuasi-symmetric 3-designs with a fixed block intersection number
Quasi-symmetric 3-designs with block intersection numbers x, y (0 ≤ x ≤ y < k) are studied. It is proved that the parameter λ of a quasi-symmetric 3-(v, k, λ) design satisfies a quadratic whose coefficients are polynomial functions of k, x and y. We use this quadratic to prove that there exist finitely many quasi-symmetric 3-designs under either of the following two restrictions: 1. The block i...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1988
ISSN: 0097-3165
DOI: 10.1016/0097-3165(88)90050-7