Water with a low pH can be described as "acidic" water. How would you refer to water with a high pH?
I would guess it's "alkalitic" or "alkalinic," but I can't find any references to those words at Dictionary.com.
The commonly used antonym of acid is alkali, of acidic is alkaline. As you mention, acid/acidic refer to pH less than 7, alkali/alkaline to pH greater than 7, and neutral to pH equal to 7. In a long scientific career I have never met the term alkalitic and extremely rarely the term alkalinic.
"Basic" is the term for substances that are bases, opposite to substances that are "acidic", or acids.
Strong bases can be described as
Caustic. In Chemistry the word is reserved for those bases 'capable of burning, corroding, or destroying living tissue'. Although
Alkaline are opposites of acidic as well, sometimes the stronger term is used for extra effect.
Here's a Google Ngram comparing the prevalence of caustic to alkaline, and two obscure terms from other answers: alkalic and alkalinic.
Alkaline or basic are the words to describe water with a high pH (That's how we've always described substances with a high pH in all my chemistry classes)
However, if you feel like you need an antonym with a closer equivalent to 'acidic' try alkalic
The word opposite of acidic would be basic.
A SOLUTION with low pH is considered acidic. A solution with a high pH is considered basic. Conversely, a solution with a low pOH is considered basic. A solution with a high pOH is considered acidic.
Alkalinity is not the same property as basicity. Basicity describes the ratio of concentrations of H3O+ to OH- in a soution. Alkalinity describes a solution's ability to neutralize H+, regardless of pH/ pOH.