Nested Optimal \lambda-Packings and \lambda-Coveringsof Pairs with Triples

  • Authors:

  • Nabil Shalaby;Jianxing Yin

  • Affiliations:

  • Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John‘s, NF, Canada A1C 557;Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 1998

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Abstract

We say that an optimal \la-packing( \la-covering) of pairs with triples can be nestedif it is possible to add one point to each block such that anoptimal 2 \la-packing (2 \la-covering)of pairs with quadruples is obtained. A packing (covering) oforder v can exist only if v \geq 4and \lfloor v / 3 \lfloor \la(v - 1) / 2 \rfloor \rfloor= \lfloor v / 4 \lfloor 2\la(v - 1) / 3 \rfloor \rfloor ( \lceilv / 3 \lceil \la(v - 1) / 2\rceil \rceil = \lceil v / 4 \lceil2\la (v - 1) / 3 \rceil \rceil ). It is shown in thispaper that this condition is also sufficient, except possiblyfor v = 20.