Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Here is a resolvable Steiner quintuple system. Every tuple from 1-25 appears in exactly one of the sets.

It's possible to cover this as a point system with ellipses and circles. An optimal covering would be one where each ellipse and circle clearly went through exactly 5 points, and didn't come close to any others. Is there a good way to optimize this?

ellipse covering of Steiner system

share|cite|improve this question

This incidence structure is not a Steiner quintuple system (they can only exist when $v=3,5\pmod{6}$). What you have is a $2$-design, and in particular a $(25,5,1)$-BIBD.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.