The maximum size of a partial 3-spread in a finite vector space over GF(2)

Let n 3 be an integer, let Vn(2) denote the vector space of dimension n over GF(2), and let c be the least residue of n modulo 3. We prove that the maximum number of 3-dimensional subspaces in Vn(2) with pairwise intersection {0} is 2n -2c 7 - c for n 8 and c = 2. (The cases c = 0 and c = 1 have already been settled.) We then use our results to construct new optimal orthogonal arrays and (s, k, )-nets.

• Type: Journal
• Year: 2010
• Where: DCC
• Authors: Saad El-Zanati, H. Jordon, G. F. Seelinger, Papa Sissokho, L. E. Spence
• Keywords: 3-dimensional Subspaces, Computer Graphics, DCC 2010, Maximum Number, Vector Space