Talk:Equiangular lines

Unclear sentence

The introduction contains this sentence:

"This upper bound is tight up to a constant factor to a construction by de Caen."

I cannot make any sense of the way this is worded. What does

"tight up to a constant factor to a construction" mean? I cannot even guess.

I hope someone knowledgeable about this subject can rephrase this sentence so that its meaning becomes clear.

The known numbers are nice, but even nicer would be another line

One sentence in the introductory section reads as follows:

"The maximum in dimensions 1 through 16 is listed in the On-Line Encyclopedia of Integer Sequences as follows:

1, 3, 6, 6, 10, 16, 28, 28, 28, 28, 28, 28, 28, 28, 36, 40, ... (sequence A002853 in the OEIS)."

This would be even nicer if someone added the line denoting the dimension of the euclidean space, which would read in order 1, 2, 3, ..., 16. (Preceding the line displayed above, with 1 above 1, 2 above 3, ..., 16 above 40.) And the lines would be displayed following labels on their left: Dimension, and # of lines.

I hope someone can turn this into a 2 × 16 table, which would be distinctly helpful to the reader.