Minimal coverings of 0,1,2n with spheres of radius n - Kolev, Emil; Baicheva, Tsonka (Utilitas Mathematica, 2017)
Consider the set Qn = 0,1,2n equipped with the usual Hamming distance. Denote by T(n) the minimal number of spheres of radius n needed to cover Qn- The exact values of T(n) are known for n ≤ 8. The first undecided case is n = 9 and it is known that 67 ≤ T(9) ≤ 68. We settle the case by showing that T(9) = 68. The inequality T(9) = 68 implies T( 10) ≥ 102, T(11) ≥ 153, T(12) ≥ 230 and T(13) ≥ 345 thus improving the best known lower bounds for 10 ≤ n ≤ 13. © 2015 Utilitas Mathematics.