Playground

Large-q explorer

Singer's construction needs no search, so it scales. Pick any prime power q up to 1024 and a background thread writes down a (q² + q + 1, q + 1, 1) difference set: for q = 1024 that is 1,025 numbers out of 1,049,601. The picture draws a chord between every two members; the tally checks every one of the differences, and each nonzero residue turns up exactly once.

The set is the list of i for which the trace of αⁱ is zero, where α generates the field with q³ elements, exactly as in Lesson 14. The link in your address bar keeps q, so you can share a view. For why the search in the search versus construction playground can't reach these sizes, see Lesson 17.