Improvement of Bruck's completion theorem

✍ Scribed by Klaus Metsch

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 1014 KB
• Volume: 1
• Category: Article
• ISSN: 0925-1022
• DOI: 10.1007/bf00157614

✦ Synopsis

Improving Bruck's Completion-Theorem for nets, we show that a net of order k and degree k + 1 -t5 can be extended to an affine plane, if 3k > 8t53 -18t52 + 8~5 + 4. As applications we obtain the following two theorems: A maximal partial t-spread in PG(2t + 1, q), q not a square, with deficiency ~ > 0 satisfies 863 -18/f 2 + 86 + 4 > 3q 2. There exists an absolute constant c such that every linear space with constant point degree n + 1 and minimum line degree n + 1 -a can be embedded in a projective plane of order n provided that n > ca 3.