in the invasion of the Spanish Netherlands in May of the same year, fewer than 15,000 remained a month later. Throughout the war, both sides struggled to support offensives outside their own boundaries; the Spanish invasion of northern France in 1636 collapsed due to lack of supplies and was not repeated. Including those supplied by Bernard of Saxe-Weimar and paid by France, between 1635 and 1642 official troop levels averaged 150,000 to 160,000, with a peak of 211,000 in 1639. These are based on official muster rolls and should be treated with caution, since officers were paid for numbers reported, rather than those actually present; in addition, during this period on average another 10% was absent due to sickness, although most generally recovered. Parrott estimates variances between "Reported" and "Actual" averaged up to 35% for the French and 50% for the Spanish. Historian John A. Lynn suggests an average of 60% "Reported" versus "Actual" "provides the most reasonable guide", a figure based on André Corvisier's 1964 work L'armée française de la fin du XVIIe siècle au ministère de Choiseul. Throughout the war, logistics remained the major constraint on the number of troops, while strategy was often subordinated to the need to find adequate provisions, especially given the primitive infrastructure then available. It was not until the 1660s that Louvois created the support systems that allowed France to sustain an army of nearly 200,000 men for extended periods, and crucially ensure co-ordinated strategy between different fronts. The more experienced Spanish were better equipped in this respect while their resources made it easier to replace losses of men and material. These advantages could be offset by engaging them on multiple fronts while attacking their lines of communication, a tactic the French used throughout the war by supporting the Catalan, Neapolitan and Portuguese rebels along with allies in Northern Italy and the Rhineland. Loss of Dutch naval support after 1648 severely impacted their ability to challenge the Spanish at sea, until replaced with the English alliance in 1657. At its peak in 1632, the Spanish army contained around 300,000 regulars, exclusive of local militia and the empire increasingly relied on its Italian territories for recruits and money. Historian Davide Maffi calculates the Duchy of Milan provided an annual 6 million scudi for the war, as well as an average of 4,000 recruits per year. The Grand Duchy of Tuscany, a de facto Spanish