Is there a conjecture such that if the conjecture holds then the following (1) and (2) hold ?(1)The worst case time complexity of k-SAT with n variables and m clauses reaches the maximum value, if m is Cn where C is a constant.  (2)The exponential time hypothesisThis question comes from a view about input size of problems. For example, an instance of 3-SAT with n variables is a 3CNF formula and the length of the formula  could be O(n^3). The complexity of obvious algorithm for 3-SAT with n variables is 2^n. 2^n is strictly smaller than 2^{ O(n^3) }. The complexity is defined as the function of input size like the length of formula and the exponential function of input length is 2^{ O(n^3) } and is not 2^n. 2^n time seems to be a sub-exponential time if the statement (1) does not hold.   
How the Number of Clauses Change the Complexity of Worst Case k-SAT ?
cc.complexity theory;sat