Direct Constructions for General Families of Cyclic Mutually Nearly Orthogonal Latin Squares


Demirkale F. , DONOVAN D., KHODKAR A.

JOURNAL OF COMBINATORIAL DESIGNS, cilt.23, ss.195-203, 2015 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 23 Konu: 5
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1002/jcd.21394
  • Dergi Adı: JOURNAL OF COMBINATORIAL DESIGNS
  • Sayfa Sayısı: ss.195-203

Özet

Two Latin squares L=[l(i,j)] and M=[m(i,j)], of even order n with entries {0,1,2,...,n-1}, are said to be nearly orthogonal if the superimposition of L on M yields an nxn array A=[(l(i,j),m(i,j))] in which each ordered pair (x,y), 0x,yn-1 and xy, occurs at least once and the ordered pair (x,x+n/2) occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders 48k+14, 48k+22, 48k+38, and 48k+46. The techniques employed are based on the principle of Methods of Differences and so we also establish infinite classes of quasi-difference sets for these orders.