The existence of symmetric skew balanced starters for odd prime powers.

Strong starters and skew starters have been widely used in various combinatorial designs such as Room squares and Howel designs. Mullin and Nemeth, also Chong and Chan, gave a construction of skew starters for every odd prime power n. Skew balanced starters and symmetric skew balanced starters are two special types of skew starters crucially used in the construction of completely balanced Howell rotations for bridge tournaments (which is different from Howell designs and whose construction remains open problem). Represent an odd prime power n as ek + 1 where e = 2(m) and k is odd. Recently, Du and Hwang gave a construction for symmetric skew balanced starters for general m >= 2 but could prove its validity only for k >= O(e(3)). Yu and Hwang improved this result to k >=O(e) and conjectured that the construction is valid for all k and k > 1. In this paper we prove the conjecture except for the two cases k = 3,9.