A New Lower Bound for the Football Pool Problem for Six Matches

In the football pool problem one wants to minimize the cardinality of a ternary code, C⊆F3n, with covering radius one, and the size of a minimum code is denoted by σn. The smallest unsettled case is 63⩽σ6⩽73. The lower bound is here improved to 65 in a coordinate-by-coordinate backtrack search using the LLL algorithm and complete equivalence checking of subcodes.