Distances of group tables and latin squares via equilateral triangle dissections

Denote by gdist(p) the least non-zero number of cells that have to be changed to get a latin square from the table of addition modulo p. A conjecture of Drápal, Cavenagh and Wanless states that there exists c>0 such that gdist(p)⩽clog(p). In this paper the conjecture is proved for c≈7.21, and as an intermediate result it is shown that an equilateral triangle of side n can be non-trivially dissected into at most 5log2(n) integer-sided equilateral triangles. The paper also presents some evidence which suggests that gdist(p)/log(p)≈3.56 for large values of p.