New results on maximal partial line spreads in PG(5,q)

TL;DR

This paper establishes new theoretical and computational results on the sizes of maximal partial line spreads in projective space PG(5,q), including existence proofs and size classifications for small q.

Contribution

It proves the existence of certain maximal partial line spreads in PG(5,q) and provides computational data for their sizes for small q, expanding known classifications.

Findings

Existence of maximal partial line spreads of size q^3+q^2+kq+1 for specified k.

Computational determination of largest sizes for q ≤ 7.

New classifications of maximal partial line spreads for q ≤ 5.

Abstract

In this work, we prove the existence of maximal partial line spreads in PG(5,q) of size q^3+q^2+kq+1, with 1 \leq k \leq (q^3-q^2)/(q+1), k an integer. Moreover, by a computer search, we do this for larger values of k, for q \leq 7. Again by a computer search, we find the sizes for the largest maximal partial line spreads and many new results for q \leq 5.