Journal of Combinatorial Mathematics and Combinatorial Computing, 49 (2004) pp.9-31.
Abstract:
In a previous article on caps in PG(5,3) and PG(6,3), it was proven that every 53-cap in PG(5,3) is contained in the 56-cap of Hill and that there exist complete 48-caps in PG(5,3). The first result was used to lower the upper bound on m_{2}(6,3) from 164 to 154. Presently, the known upper bound on m_{2}(6,3) is 148. In this article, using computer searches, we prove that every 49-cap in PG(5,3) is contained in a 56-cap, and that every 48-cap, having a 20-hyperplane with at most 8-solids, is also contained in a 56-cap. These computer results enable us to present a geometrical proof that m_{2}(6,3) ‹= 147. A computer search for caps in PG(6,3) which uses the computer results of PG(5,3) then lowers this upper bound to m_{2}(6,3) ‹= 136. So now we know that 112 ‹= m_{2}(6,3) ‹= 136.
Download the paper as pdf.
| home | List of publications |