What Makes Absinthe "Supérieure"?

I want to see if an absinthe cocktail needs an expensive absinthe to be the best. Or can you just use an absinthe like liqueur or cheap absinthe. I make three cocktails named Green Beast to find out. Green Beast Absinthe 1oz Simple syrup 1oz Lime juice 1oz Chilled water 4oz Cucumber slices Cheap absinthe version $0.72 Cristiani Parnasse Absinthe $0.02 Simple syrup $0.38 Lime juice $0.10 Cucumber $1.22 TOTAL Liqueur Version $1.44 Pernod Liqueur $0.02 Simple syrup $0.38 Lime juice $0.10 Cucumber $1.94 TOTAL Expensive absinthe version $4.00 Pernod 68 Absinthe $0.02 Simple syrup $0.38 Lime juice $0.10 Cucumber $4.50 TOTAL