This data gives the singly generated standard integral table algebras of ranks $4, 5, 6,$ and $7$ up to a different order and valency depending on each rank. The following notation has been used in the Existence column in the Markdown Table:
AS: the program constructed a scheme for this parameter set. So those are realizable as Association schemes.
TA-xHL: table algebra that failed the handshaking lemma, so program could not start.So, they are not realizable.
TA-xIM: table algebra that failed the integral multiplicity condition.
TA-xR: table algebra that is not realizable by the classification or because it fails some other feasibility condition.
O: table algebra that passes the feasibility conditions and the realizability is still open.
For rank 4 database please see https://roghayehmaleki.github.io/QPG-database/Rank4SsinglegeneratorSITAs/html-file.html
For rank 5 database please see https://roghayehmaleki.github.io/QPG-database/Rank5SsinglegeneratorSITAs/html-file.html
For rank 6 database please see https://roghayehmaleki.github.io/QPG-database/Rank6SsinglegeneratorSITAs/html-file.html
For rank 7 database please see https://roghayehmaleki.github.io/QPG-database/Rank7SsinglegeneratorSITAs/html-file.html