Implementation Policies

(Under development)

The external representation for block designs gives the implementor a great deal of choice about what to include when specifying a block design and its properties. Here we record our policies about what (and what not) to include in certain cases:

How far to go with point_concurrences?

If the given block design is not a $t$-design (with $t \geq 2$), then include the $k$-wise point concurrences only for $k = 1$ and (unless there is just one point) $k = 2$. In both cases, the full preimage should be given (which may be entire_domain). This policy gives the replication number for each point and the pairwise point concurrences. If the given block design $D$ is a $t$-design (with $t = 2$) then include the $k$-wise point concurrences for $k = 1,2, \ldots ,max(t)$ for which $D$ is a $t$-design. Again, full preimages should be given and they are all, of course, entire_domain.

How far to go with block_concurrences?

Include the $k$-wise block concurrences for $k = 1$ and (unless there is just one block) $k = 2$. In both cases, preimages should be collapsed to preimage cardinalities. This policy gives the sizes of the blocks, the number of blocks of each size, the sizes of the pairwise intersections of blocks, and the number of pairs of blocks giving each intersection size.

How far to go with t_wise_balanced?

This is analogous to point_concurrences. If the given block design $D$ is not a $t$-design (with $t = 2$), then normally include whether or not $D$ is $t$-wise balanced only for $t = 1$ and $t = 2$. Otherwise, include this information for $t = 1,2, \ldots, max(t)$ for which $D$ is a $t$-design. Note that this maximum $t$ is recorded in the t_design indicator.