Heden's bound on maximal partial spreads
نویسندگان
چکیده
We prove Heden’s result that the deficiency δ of a maximal partial spread in PG(3, q) is greater than 1+ 1 2 (1+ √ 5)q unless δ−1 is a multiple of p, where q = p. When q is odd and not a square, we are able to improve this lower bound to roughly √ 3q.
منابع مشابه
Partial Ovoids and Spreads in Generalized Quadrangles, and Related Combinatorial Structures
In this paper we overview what is known about partial ovoids and spreads of finite (classical) generalized quadrangles. In the first, respectively the second, part of the paper we will be mostly concerned with small, respectively large, maximal partial ovoids and spreads. Also connections with other interesting objects in finite geometry will be explained. Among the new results are new bounds o...
متن کاملOn Maximal Partial Spreads in PG(n, q)
In this paper we construct maximal partial spreads in PG(3, q) which are a log q factor larger than the best known lower bound. For n ≥ 5 we also construct maximal partial spreads in PG(n, q) of each size between cnqn−2 log q and c′qn−1.
متن کاملOn maximal partial spreads of H(2n+1, q2)
A lower bound for the size of a maximal partial spread of H(2n+1, q) is given. For H(2n + 1, q) in general, and for H(5, q) in particular, new upper bounds for this size are also obtained. In [1], maximal partial spreads of H(3, q) and H(5, q) have been constructed from spreads of W3(q) and W5(q) respectively; the construction for H(5, q) will be generalized to H(4n+ 1, q), n ≥ 1, thus yielding...
متن کاملPartial ovoids and partial spreads in hermitian polar spaces
We present improved lower bounds on the sizes of small maximal partial ovoids in the classical hermitian polar spaces, and improved upper bounds on the sizes of large maximal partial spreads in the classical hermitian polar spaces. Of particular importance is the presented upper bound on the size of a maximal partial spread of H(3,q2). For q = 2, 3, the presented upper bound is sharp. For q = 3...
متن کاملConstant Rank-Distance Sets of Hermitian Matrices and Partial Spreads in Hermitian Polar Spaces
In this paper we investigate partial spreads of H(2n− 1, q2) through the related notion of partial spread sets of hermitian matrices, and the more general notion of constant rank-distance sets. We prove a tight upper bound on the maximum size of a linear constant rank-distance set of hermitian matrices over finite fields, and as a consequence prove the maximality of extensions of symplectic sem...
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:
- Discrete Mathematics
دوره 74 شماره
صفحات -
تاریخ انتشار 1989