The maximum size of a partial spread II: Upper bounds

Let $n$ and $t$ be positive integers with $t 2$. The exact value of the maximum size partial $(t-1)$-spread has been recently determined for $t>{\theta}_r$ by the authors of this paper (see Năstase-Sissokho [21]).

[1]  J. Schönheim,et al.  Group Partition, Factorization and the Vector Covering Problem , 1972, Canadian Mathematical Bulletin.

[2]  P. Dembowski.  Finite geometries , 1997 .

[3]  Johannes André,et al.  Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe , 1954 .

[4]  Beniamino Segre,et al.  Teoria di Galois, fibrazioni proiettive e geometrie non desarguesiane , 1964 .

[5]  Alberto Ravagnani,et al.  Partial spreads in random network coding , 2014, Finite Fields Their Appl..

[6]  András Gács,et al.  On Maximal Partial Spreads in PG(n, q) , 2003, Des. Codes Cryptogr..

[7]  Sascha Kurz.  Improved upper bounds for partial spreads , 2017, Des. Codes Cryptogr..

[8]  Albrecht Beutelspacher,et al.  Partial spreads in finite projective spaces and partial designs , 1975 .

[9]  Dieter Jungnickel,et al.  A note on maximal partial spreads with deficiency q+1, q even , 2003, J. Comb. Theory, Ser. A.

[10]  Alexander Vardy,et al.  Error-correcting codes in projective space , 2008, 2008 IEEE International Symposium on Information Theory.

[11]  Papa Sissokho,et al.  The maximum size of a partial spread in a finite projective space , 2016, J. Comb. Theory, Ser. A.

[12]  Tuvi Etzion,et al.  Problems on q-Analogs in Coding Theory , 2013, ArXiv.

[13]  Alfred Wassermann,et al.  Tables of subspace codes , 2016, ArXiv.

[14]  Se June Hong,et al.  A General Class of Maximal Codes ror Computer Applications , 1972, IEEE Transactions on Computers.

[15]  David A. Drake,et al.  Partial t-spreads and group constructible (s,r,μ)-nets , 1979 .

[16]  Olof Heden,et al.  Some necessary conditions for vector space partitions , 2011, Discret. Math..

[17]  Heather Jordon,et al.  The maximum size of a partial 3-spread in a finite vector space over GF(2) , 2010, Des. Codes Cryptogr..

[18]  Leo Storme,et al.  On the Spectrum of the Sizes of Maximal Partial Line Spreads in PG(2n,q), n ≥ 3 , 2005, Des. Codes Cryptogr..

[19]  Tuvi Etzion.  Perfect Byte-Correcting Codes , 1998, IEEE Trans. Inf. Theory.

[20]  Tuvi Etzion,et al.  Galois geometries and coding theory , 2016, Des. Codes Cryptogr..

[21]  Olof Heden.  On the length of the tail of a vector space partition , 2009, Discret. Math..

[22]  Olof Heden,et al.  A Survey of the Different Types of Vector Space Partitions , 2011, Discret. Math. Algorithms Appl..

[23]  Sascha Kurz.  Upper bounds for partial spreads , 2017 .

[24]  Alexander Vardy,et al.  Error-Correcting Codes in Projective Space , 2011, IEEE Trans. Inf. Theory.