More on the existence of small quasimultiples of affine and projective planes of arbitrary order

The functions a(n) and p(n) are defined to be the smallest integer λ for which λ‐fold quasimultiples affine and projective planes of order n exist. It was shown by Jungnickel [J. Combin. Designs 3 ( 6 ), 427–432] that a(n),p(n) < n¹⁰ for sufficiently large n. In the present paper, we prove that a(n),p(n) < n³. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 182–186, 2001