# Increase of _Trichoderma harzianum_ Production Using Mixed-Level Fractional Factorial Design
## 1 Introduction
A method using polynomial counting, based on complex level counting for quadratic optimization, was shown [17]. An algorithm to create matrices of mixed levels of generalized minimum aberration using mixed integer optimization with quadratic conic constraints was presented [18]. These methods require great computational skills and statistical knowledge, which overly complicates their application in industry [11; 13]. An alternative to these complex algorithms is provided with the NOBA and NONBPA methods [19; 20]. The NOBA method was elaborated to generate orthogonal and near-orthogonal balanced mixed-level fractional factorial designs. The NOBA method allows us to optimize the process using fewer runs while ensuring that balance and orthogonality properties are maintained as much as possible in the resulting fraction [19]. The authors developed the NONBPA (Near-Orthogonal Pure array) method for those designs that, due to their nature, once fractionated, present difficulty in possessing the balance property. NOBA and NONBPA methods are less expensive and easier to apply in the industry and can be adapted to any production process [20]. This document shows the maximization of the production process of _Trichoderma harzianum_ by making use of the NOBA method. The experimental design involved the following factors:  
* Air. Occasional aeration allows good growth and sporulation of the fungus. Concentrations of carbon dioxide in the air higher than 10-15%, a product of cellular respiration, inhibit growth [21];
* Humidity. The amount of water that permeates the environment where the fungus develops is another key characteristic [22]. Trichoderma presents a low level of osmotic tolerance; an excess of humidity lowers the availability of oxygen, limiting the development of the fungus, and compacting the substrate, preventing their full colonization. On the other hand, low humidity inhibits the development of fungus by limiting the mobility of nutrients [23];* Temperature. This magnitude, referring to the notion of heat, impacts the physiology of fungal growth and is evidenced by the inhibition in the elongation of the hypha, the decrease in the germination of the conidia, and the formation of the germinal tube. For this reason, this factor limits the development of microorganisms [22];
* pH. The measure of acidity or alkalinity is important for Trichoderma species; however, they are not demanding in relation to the pH of the substrate. They can grow in a wide pH range [24];
* Substrate. Any solid material other than soil in situ, natural, synthetic, residual, mineral, or organic, which, placed in a container, in pure form, or in a mixture, allows the anchorage of the root system [25]. It is worth mentioning that in this work, the incubation period and the inoculum concentration are factors that remained fixed at 28 days and 10%, respectively. Technological and development costs are major challenges for the development of industrial products [22]. Colonies of _Trichoderma harzianum_ grow and mature rapidly after five days of incubation on a potato dextrose agar culture medium. In a previous design of 28 runs, the laboratory found an increase in the spore's growth of 50% during the 21 days and 250% during the 28 days of incubation, realizing that in the 29 days onwards, the mass began to decrease. There are various forms of production of Trichoderma harzianum, solid, liquid, and biphasic. The biphasic is the fastest, because the inoculum is produced by liquid fermentation, which is then used to ferment the solid substrate [26]; in addition, it has been reported that substances that promote plant growth, such as indoleacetic acid, gibberell acid, cytokins, and vitamins are produced in a liquid medium [27].