Here's the revised code, based on the suggestions from code reviews, excluding @arekolek's answer, which appears to be a review of this revised code here.

from random import randrange
from bisect import bisect_left


def randomList(N, max):
    return [randrange(max) for x in xrange(N)]


def subsequence(seq):
    """Returns the longest subsequence (non-contiguous) of seq that is
    strictly increasing.

    """
    # head[j] = index in 'seq' of the final member of the best subsequence 
    # of length 'j + 1' yet found
    head = [0]
    # predecessor[j] = linked list of indices of best subsequence ending
    # at seq[j], in reverse order
    predecessor = [-1]
    for i in xrange(1, len(seq)):
        ## Find j such that:  seq[head[j - 1]] < seq[i] <= seq[head[j]]
        ## seq[head[j]] is increasing, so use binary search.
        j = bisect_left([seq[head[idx]] for idx in xrange(len(head))], seq[i])

        if j == len(head):
            head.append(i)
        if seq[i] < seq[head[j]]:
            head[j] = i
 
        predecessor.append(head[j - 1] if j > 0 else -1)

    ## trace subsequence back to output
    result = []
    trace_idx = head[-1]
    while (trace_idx >= 0):
        result.append(seq[trace_idx])
        trace_idx = predecessor[trace_idx]

    return result[::-1]


l1 = randomList(15, 100)

Here's the revised code, based on the suggestions from code reviews, excluding @arekolek's answer, which appears to be a review of this revised code here.

from random import randrange
from bisect import bisect_left


def randomList(N, max):
    return [randrange(max) for x in xrange(N)]


def subsequence(seq):
    """Returns the longest subsequence (non-contiguous) of seq that is
    strictly increasing.

    """
    # head[j] = index in 'seq' of the final member of the best subsequence 
    # of length 'j + 1' yet found
    head = [0]
    # predecessor[j] = linked list of indices of best subsequence ending
    # at seq[j], in reverse order
    predecessor = [-1]
    for i in xrange(1, len(seq)):
        ## Find j such that:  seq[head[j - 1]] < seq[i] <= seq[head[j]]
        ## seq[head[j]] is increasing, so use binary search.
        j = bisect_left([seq[head[idx]] for idx in xrange(len(head))], seq[i])

        if j == len(head):
            head.append(i)
        if seq[i] < seq[head[j]]:
            head[j] = i
 
        predecessor.append(head[j - 1] if j > 0 else -1)

    ## trace subsequence back to output
    result = []
    trace_idx = head[-1]
    while (trace_idx >= 0):
        result.append(seq[trace_idx])
        trace_idx = predecessor[trace_idx]

    return result[::-1]


l1 = randomList(15, 100)