Admissible parameters of symmetric designs satisfying and symmetric designs with inner balance

作者：Broughton Wayne^*

来源：Designs, Codes and Cryptography, 2014, 73(1): 77-83.

DOI：10.1007/s10623-013-9810-y

• Symmetric designs
• Pseudo quasi-3
• Quasi-symmetric
• Inner balance
• Triple arrays

The admissible parameters of symmetric (v, k, lambda) designs satisfying nu = 4 (k -lambda ) + 2 are shown to correspond with the solutions of a certain Pell equation. We then determine the feasible parameters of such designs that could have a quasi-symmetric residual design with respect to a block, and classify them into two possible families. Finally, we consider the feasible parameters of symmetric designs with inner balance as defined by Nilson andHeidtmann (Des. Codes Cryptogr. doi:10.1007/s10623-012-9730-2, (2012)), and show that (with one exception) they must all belong to one of these families.

• 出版日期2014-10