## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 40, Number 3 (2011), 431-447.

### A characterization of 42 ovoids with a certain property in *PG*(3,2)

#### Abstract

In this paper, we characterize 42 ovoids with a certain property in a projective space *PG*(3,2) described in Yucas [6]. As a corollary, we construct the Steiner 4-wise balanced design *S*(4,{5,6},17) with 252 blocks which is an extension of the point-plane design * A* of an affine space

*AG*(4,2). The construction leads to not only the uniqueness of such an extension, but also a (usual) extension of the 2-repeated design 2.

*.*

**A**#### Article information

**Source**

Hokkaido Math. J., Volume 40, Number 3 (2011), 431-447.

**Dates**

First available in Project Euclid: 26 October 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1319595865

**Digital Object Identifier**

doi:10.14492/hokmj/1319595865

**Mathematical Reviews number (MathSciNet)**

MR2883500

**Zentralblatt MATH identifier**

1233.51002

**Subjects**

Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 05B25: Finite geometries [See also 51D20, 51Exx]

**Keywords**

Steiner 4-wise balanced design affine space orthogonal group exterior algebra alternating forms quadratic forms

#### Citation

INOUE, Koichi. A characterization of 42 ovoids with a certain property in PG (3,2). Hokkaido Math. J. 40 (2011), no. 3, 431--447. doi:10.14492/hokmj/1319595865. https://projecteuclid.org/euclid.hokmj/1319595865