In search of 4-(12, 6, 4) designs: Part I
نویسندگان
چکیده
Martin J. Sharry and Anne Penfold Street, Centre for Combinatorics, Department of Mathematics, The University of Queensland, Brisbane 4072, Australia. As a first step towards finding all 4-(12, 6, 4) designs which are not 5-(12, 6, 1) designs, it is shown that if such a design has a pair of blocks with five points in common, then there is a unique way of assigning the replicas of the seven points from that pair of blocks to the other blocks of the design.
منابع مشابه
In search of 4-(12, 6, 4) designs: Part III
A 4-(12, 6, 4) design that is not also a 5-(12, 6, 1) design must have at least one pair of blocks with five points in common. It is shown that there are just nine non-isomorphic such designs; so, including the 5-(12, 6, 1) design, there are ten 4-(12, 6, 4) designs. These designs are characterised by the orders of their automorphism groups and they all contain a 4-(11, 5, 1) design.
متن کاملIn search of 4-(12, 6, 4) designs: Part II
In a 4-(12, 6, 4) design a block is either disjoint from one other block or it has five points in common with one other block. For a 4-(12, 6, 4) design with a pair of blocks of the second type it is shown that· another thirty blocks of the design can be completed in a unique way and these thirty blocks contain a copy of a 3-(10, 4, 1) design.
متن کاملUsing Kullback-Leibler distance for performance evaluation of search designs
This paper considers the search problem, introduced by Srivastava cite{Sr}. This is a model discrimination problem. In the context of search linear models, discrimination ability of search designs has been studied by several researchers. Some criteria have been developed to measure this capability, however, they are restricted in a sense of being able to work for searching only one possibl...
متن کاملNew infinite families of 3-designs from preparata codes over Z4
We consider t-designs constructed from codewords in the Preparata code ~ ove r 2~4. A new approach is given to prove that the support (size 5) of minimum Lee weight codewords form a simple 3-design for any odd integer m >t 3. We also show that the support of codewords with support size 6 form four new families of simple 3-designs, with parameters (2",6,2" 8 ) , (2",6,5 (2 m-I 4)), (2m,6,20 • (2...
متن کاملThe parameters 4-(12, 6, 6) and related t-designs
It is shown that a 4-(12,6,6) design, if it exists, must be rigid. The intimate relationship of such a design with 4-(12,5,4) designs and 5-(12,6,3) designs is presented and exploited. In this endeavor we found: (i) 30 nonisomorphic 4-(12,5,4) designs; (ii) all cyclic 3-(11,5,6) designs; (iii) all 5-(12,6,3) designs preserved by an element of order three fixing no points and no blocks; and (iv)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 7 شماره
صفحات -
تاریخ انتشار 1993