A086676 Number of n-dimensional 2 X 2 X ... X 2 grid graphs needed to cover an n-dimensional 3 X 3 X ... X 3 torus.
2, 3, 5, 8, 12, 18, 29, 44, 68
Offset: 1
Keywords
Examples
Known bounds for n=10 through 13, from Kolev (2014): 10 102-104 11 153-172 12 230-264 13 345-408
References
- Patric R. J. Östergård and T. Riihonen, A covering problem for tori, Annals of Combinatorics, 7 (2003), 1-7.
Links
- D. Brink, The Inverse Football Pool Problem, J. Int. Seq. 14 (2011) # 11.8.8.
- Emil Kolev, Covering of {F_3}^n with spheres of maximal radius, Fourteenth International Workshop on Algebraic and Combinatorial Coding Theory, September 7-13, 2014, Svetlogorsk (Kaliningrad region), Russia pp. 198-203.
- E. Kolev and T. Baicheva, About the inverse football pool problem for 9 games, Seventh International Workshop on Optimal Codes and Related Topics, September 6-12, 2013, Albena, Bulgaria pp. 125-133.
- Patric R. J. Östergård, Home page
Extensions
I have added two terms (29 and 44). The ranges for the next terms are [66,68] and [99,104]. David Brink, Jun 03 2009
For a(9) = 68 and further bounds see Kolev and Baicheva. - N. J. A. Sloane, Mar 10 2014