Several new lower bounds for football pool systems (Q2713661)

A ternary covering code \(C\) of length \(n\) and radius \(R\) is a collection of ternary vectors of length \(n\) with the property that every ternary vector of length \(n\) differs from at least one codeword of \(C\) in at most \(R\) coordinates. Let \(K_3(n,R)\) be the minimal size of a ternary covering code \(C\) of length \(n\) and radius \(R\). The following lower bounds are proved: NEWLINE\[NEWLINE K_3(6,2)\geq 14, K_3(7,3)\geq 9, K_3(8,2)\geq 54, K_3(8,3)\geq 14. NEWLINE\]NEWLINE These results improve the best previously known bounds of 12, 7, 52 and 13, respectively.