University of Waterloo I began my M.Math. (Thesis Option) program at the University of Waterloo’s Computer Science Department in the fall of 1988. Charlie Colbourn served as my adviser.

I completed the following courses in fulfillment of the course requirements:

I entered the M.Math. program choosing network reliability as my thesis topic. But that changed almost immediately. Kreher and Radziszowski had then recently discovered the application of Lovasz’s basis reduction algorithm for constructing t-designs. Knowing that I had some familiarity with Lovasz’s algorithm from two courses I had taken in my undergraduate studies, Charlie passed me Kreher and Radziszowski’s paper to read. I learned the definition of a t-design from that paper and easily understood the algorithm there because it is an extension and refinement of an algorithm of Lagarias and Odlyzko for solving subset sum problems that Ron Mullin had showed me just the term before.

With their method, Kreher and Radziszowski had constructed the first simple 6-design known. I was quite surprised that very few simple t-designs were known for t > 3. I remember vividly telling Charlie that I wanted to construct a simple 7-design! That was the beginning of my career in design theory and I haven’t left it since!

Charlie provided all the necessary encouragement and guidance for this project. He introduced me to Don Kreher who generously sent me a copy of his “Design Theory Toolchest” on a 5-1/4 inch floppy. I did not have a PC then, so I went to a classmate’s apartment to use his PC in order to ftp the software to the school’s computer. I remember the excitement in getting the software going and constructing my first example of a 2-(7,3,1) design.

Charlie, Don, and myself also undertook a comprehensive survey on the existence of simple t-designs with 30 or less points. This survey was later published in Ars Combinatoria and became quite widely-cited.

Simultaneously, I was trying to construct as many t-designs as I can, whose existence were unknown, in order to fill in the survey. Almost everyday, I would be in the computer labs until the wee hours of the morning constructing t-designs. I had much success by considering various automorphism groups.

Then Charlie posed an interesting question! He noticed that a large set of 2-(9,3,1) designs can be constructed so that each of the 7 designs in the large set is obtained from another by a cyclic shift (fixing 2 points). He asked if there are other examples of this phenomenon, which may lead to new large sets. I investigated a generalization of this problem and was able to construct a large set of 3-(13,5,15) designs, whose existence was previously unknown. With other heuristics I was also able to construct a few more new large sets. In my investigation of large sets, I also noticed that the special affine and PSL groups are extremely effective in giving large sets of 2-designs and 3-designs, respectively.

Charlie brought me along to a combinatorics seminar at Syracuse University in fall of 1988 to meet Don in order to discuss and crystallize some of these ideas. Charlie drove a red car (I can’t remember the make now) that he’s had since his student days. He was rather sentimental of the car. We had to stop throughout the trip to top up water in the radiator. But we made it to Syracuse!

I can’t recall much of the seminar except remember hearing the terms “cop-win graphs” and “cocktail party graphs”. I also met Doug Stinson and Alex Rosa for the first time. I remember sitting with Charlie and Doug and quietly observing them work on what would become their paper (with Alex Rosa) “Pairwise Balanced Designs with Block Sizes Three and Four” in the cafe of the hotel.

After the seminar, Charlie and I visited Don at Rochester Institute of Technology. We discussed my observations on large sets in the cafeteria. Don also gave me a number of reprints of his papers. One of these is his paper with Chouinard and Kramer “Graphical t-Wise Balanced Designs”. I read this paper with much interest after returning to Waterloo. Instead of fixing λ, I tried fixing t=2, 3 and k=3, 4 and determined all such graphical t-(v,k,λ) designs. I showed my results to Charlie who encouraged me to show it to Earl Kramer. This result would become my first paper accepted for publication in a journal.

In February 1989, Charlie spent some time at Auburn University and I visited him there. It was an interesting place with so many design theorists around: Dean Hoffman, Curt Lindner, Kevin Phelps, Chris Rodger, and Luc Tierlinck. Tony Hilton was also there at that time. It was nice just sitting there, chatting with them, and listening to them talk.

Sometime at the end of February 1989, we drove from Auburn University to Boca Raton to attend the Southeastern Conference on Combinatorics, Graph Theory, and Computing at the Florida Atlantic University. Rob Day took Dave Bigelow and me in his car. Both Rob and Dave were Charlie’s Ph.D. students then. We drove through the night. I took over the wheels in the middle. Sometime later, I heard a bang and the next thing I knew, Rob was shouting and I slammed on the brakes and the car made a complete 180-degree turn. I realized later that I must have fallen asleep driving and knocked into the road railings. We were all extremely lucky to escape without a scratch. If either one of the following two happened, we would have been seriously injured or worse: (1) there were cars coming on from behind; and (2) the railings were missing (because there was a rather deep ditch on the side). I can’t help thinking that God must be watching over us. Rob was devastated. He had just had his car repaired from a previous accident just a few weeks before, and now he’s got to send in to the repair shop again. *Sorry, Rob!* We continued on our journey with Rob driving, this time all three of us were wide awake!

The first talk of my academic career was given at the 1989 Southeastern Conference on Combinatorics, Graph Theory, and Computing. Charlie was very encouraging and was a real confidence booster. I also managed to show Earl Kramer my results on graphical designs and he was very encouraging. The conference was real fun. We played pool, ate rock shrimps in restaurants, crawled pubs, even participated in a trivial contest in one of the pubs (with Dave Bigelow, Rob Day, Gord Royle, & Renate Scheidler). Dave, Rob, & I took a morning off at the beaches.

When I returned to Waterloo, I was ready to write up my thesis. I spent late nights in my office during the writing, with a radio accompanying me. The occasional interruptions were time spent thinking about interesting problems that Charlie was working on. One of the problems was the support size problem for 6-fold triple systems. While thinking about this problem, I rediscovered the Kruskal-Katona problem (but not its solution).

During this period, Don and Dom de Caen visited me. This is also the first time I met Dom. He struck me as a soft-spoken gentleman on first impression. The three of us strolled along downtown King Street in Kitchener looking for dinner. After dinner, we went back to my office to try to construct some designs. I remembered both Don and Dom being very patient with explaining some group actions to me, including the wreath product. We stayed till quite late but we constructed some new designs. Sadly, Dom has recently passed away. But I will never forget that day the three of us were together.

I also collaborated with Gord Royle, who was then a post-doctoral fellow in the Department of Combinatorics & Optimization at Waterloo. I found that the basis reduction algorithm of Kreher and Radziszowski could be used to prove the nonexistence of certain designs (instead of existence)! As a result, I enumerated all the 2-rotational 2-(25,3,1) designs. Gord independently enumerated these designs and our results agreed, and thus the birth of our first joint paper “The 2-rotational Steiner triple systems of order 25”, which we submitted to a special volume of Discrete Mathematics dedicated to the memory of Egmont Kohler.

I made a presentation of my results on large sets at an American Mathematical Society’s meeting’s special session on codes & designs held at Loyola University, Chicago in May 1989. There, I met Neil Sloane for the first time. I also toured Sears Tower with Charlie and Alex Rosa, but the weather was so bad that we did not have any visibility from the top of the tower. We were at the top for less than 5 minutes before we decided to head down. We had lunch in a restaurant where Charlie ordered baked brie. That was my first introduction to a form of melted cheese different from mozarella on pizzas. Little did I know then that I would encounter even more variations of melted cheese later in Switzerland and began a long-term love for any cheese melted, whether in the form of grilled cheese, baked brie, Swiss fondue, raclette, or fried mozarella sticks.

I finished my M.Math. thesis “The Basis Reduction Algorithm And Existence of Combinatorial Designs” sometime in June 1989. The readers for my thesis were Anna Lubiw and Ron Mullin. I was awarded my M.Math. degree at the Fall 1989 Convocation, which I didn’t attend. I left Canada for Singapore in August 1989. Before I left, Charlie invited me to his house, and had dinner with his family in St. Jacobs. An unforgettable scene was Charlie playing with his daughter Sussie, while singing Bobby McFerrin’s “Don’t Worry Be Happy” along with the radio. These are wonderful memories that will forever stay with me.