Quasi-symmetric designs on $ 56 $ points

نویسندگان

چکیده

<p style='text-indent:20px;'>Computational techniques for the construction of quasi-symmetric block designs are explored and applied to case with <inline-formula><tex-math id="M2">\begin{document}$ 56 $\end{document}</tex-math></inline-formula> points. One new id="M3">\begin{document}$ (56,16,18) many id="M4">\begin{document}$ (56,16,6) discovered, non-existence id="M5">\begin{document}$ (56,12,9) id="M6">\begin{document}$ (56,20,19) certain automorphism groups is proved. The number known symmetric id="M7">\begin{document}$ (78,22,6) also significantly increased.</p>

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A note on quasi-symmetric designs

A quasi-symmetric design is a (v, k, λ) design with two intersection numbers x, y where 0 ≤ x < y < k. We show that for fixed x, y, λ with x > 1, λ > 1, y = λ and λ (4xy + ((y − x) − 2x− 2y + 1)λ) a perfect square of a positive integer, there exist finitely many quasi-symmetric designs. We rule out the possibilities of quasi-symmetric designs corresponding to y = x + 3 and (λ, x) = (9, 2), (8, ...

متن کامل

Maximal arcs and quasi-symmetric designs

In 2001, Blokhuis and Haemers gave an interesting construction for quasisymmetric designs with parameters 2-(q, q(q − 1)/2, q(q − q − 2)/4) and block intersection numbers q(q − 2)/4 and q(q − 1)/4 (where q ≥ 4 is a power of 2), which uses maximal arcs in the affine plane AG(2, q) and produces examples embedded into affine 3-space AG(3, q). We consider this construction in more detail and in a m...

متن کامل

Polarities, quasi-symmetric designs, and Hamada's conjecture

We prove that every polarity of PG(2k − 1, q), where k ≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to PGk(2k, q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. P...

متن کامل

Binary codes and quasi-symmetric designs

obtain a new for the of a-(u, A) design the block intersection designs are eliminated by an ad hoc coding theoretic argument. A 2-(v, k, A) design 93 is said to be quasi-symmetric if there are two block intersection sizes s1 and s2. The parameters of the complementary design !3* are related to the parameters of 93 as follows: Here Ai denotes the number of blocks through a given i points (and A ...

متن کامل

On quasi-symmetric designs with intersection difference three

In a recent paper, Pawale [22] investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x+ 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper, quasi-symmetric designs with y−x = 3 are investigated. It is...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Advances in Mathematics of Communications

سال: 2021

ISSN: ['1930-5346', '1930-5338']

DOI: https://doi.org/10.3934/amc.2020086