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Abstract

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  2. Abstract

The author corrects some errors in Theorem 17 of the paper entitled “On the existence of simple BIBDs with number of elements a prime power”.

This erratum presents corrections to errors in Theorem 17 of the originally published article (JCD 21(2): 47–59, 2013; DOI: 10.1002/jcd21309), and to add a paragraph for the proof of that theorem.

  1. The statements in (1)(a) and (2)(a) of Theorem 17 are modified as
    • (1)(a)
      inline image and inline image, inline image, inline image, or inline image;”
    • (2)(a)
      inline image and inline image, inline image, inline image, or inline image;”
  2. The particular situations in Theorem 17 are derived in the following.

    • (a)
      β is odd and inline image.
      1. When inline image, inline image, inline image, or inline image, we require that inline image. From this we obtain inline image.
      2. When inline image, we require that
        • display math
        We obtain inline image from the second part of this inequality. We claim that the first part of the inequality always holds. Let us consider the case when inline image.
        • display math
        Therefore, it suffices to check if inline image, i.e., inline image. When inline image, it is certainly true. As to the situation when inline image, the requirement can be checked directly: inline image. Note that we can assume inline image in the discussion.
    • (b)
      β is even and inline image.
      1. When inline image, inline image, inline image, or inline image, we require that inline image. From this we obtain inline image.
      2. When inline image, we require that
        • display math
        We obtain inline image.