$t$-wise balance

A block design is t-wise balanced if each set of $t$ distinct points is contained in a constant number of blocks; it does not imply constant block size. (The two properties together specify a $t$-design.) Unlike for $t$-designs, a block design may be $t$-wise balanced but not $s$-wise balanced for $s < t$. We store information about the values of $t$ for which the design is $t$-wise balanced as list of index_flags.

Here is an example of the t_wise_balanced element for the Fano plane:

<t_wise_balanced>
    <index_flag flag="true" index="1">
    </index_flag>
    <index_flag flag="true" index="2">
    </index_flag>
</t_wise_balanced>